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  • Articles  (2,461)
  • Springer  (2,461)
  • National Academy of Sciences
  • 1995-1999  (2,461)
  • Philosophy  (2,461)
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  • Articles  (2,461)
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  • 1
    Electronic Resource
    Electronic Resource
    Helena Rasiowa (1995)
    Springer
    Studia logica 54 (1995), S. 1-2 
    Details
    ISSN: 1572-8730
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Philosophy
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01058529
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  • 2
    Electronic Resource
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    Books received (1995)
    Springer
    Studia logica 54 (1995), S. 129-137 
    Details
    ISSN: 1572-8730
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Philosophy
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01058535
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  • 3
    Electronic Resource
    Electronic Resource
    A complete minimal logic of the propositional contents of thought (1995)
    Springer
    Studia logica 54 (1995), S. 391-410 
    Details
    ISSN: 1572-8730
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Philosophy
    Notes: Abstract Our purpose is to formulate a complete logic of propositions that takes into account the fact that propositions are both senses provided with truth values and contents of conceptual thoughts. In our formalization, propositions are more complex entities than simple functions from possible worlds into truth values. They have a structure of constituents (a content) in addition to truth conditions. The formalization is adequate for the purposes of the logic of speech acts. It imposes a stronger criterion of propositional identity than strict equivalence. Two propositions P and Q are identical if and only if, for any illocutionary force F, it is not possible to perform with success a speech act of the form F(P) without also performing with success a speech act of the form F(Q). Unlike hyperintensional logic, our logic of propositions is compatible with the classical Boolean laws of propositional identity such as the symmetry and the associativity of conjunction and the reduction of double negation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01053006
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  • 4
    Electronic Resource
    Electronic Resource
    Tableaus for many-valued modal logic (1995)
    Springer
    Studia logica 55 (1995), S. 63-87 
    Details
    ISSN: 1572-8730
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Philosophy
    Notes: Abstract We continue a series of papers on a family of many-valued modal logics, a family whose Kripke semantics involves many-valued accessibility relations. Earlier papers in the series presented a motivation in terms of a multiple-expert semantics. They also proved completeness of sequent calculus formulations for the logics, formulations using a cut rule in an essential way. In this paper a novel cut-free tableau formulation is presented, and its completeness is proved.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01053032
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  • 5
    Electronic Resource
    Electronic Resource
    Averaging the truth-value in Łukasiewicz logic (1995)
    Springer
    Studia logica 55 (1995), S. 113-127 
    Details
    ISSN: 1572-8730
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Philosophy
    Notes: Abstract Chang's MV algebras are the algebras of the infinite-valued sentential calculus of Łukasiewicz. We introduce finitely additive measures (called states) on MV algebras with the intent of capturing the notion of ‘average degree of truth’ of a proposition. Since Boolean algebras coincide with idempotent MV algebras, states yield a generalization of finitely additive measures. Since MV algebras stand to Boolean algebras as AFC*-algebras stand to commutative AFC*-algebras, states are naturally related to noncommutativeC*-algebraic measures.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01053035
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  • 6
    Electronic Resource
    Electronic Resource
    Undefinability of propositional quantifiers in the modal system S4 (1995)
    Springer
    Studia logica 55 (1995), S. 259-271 
    Details
    ISSN: 1572-8730
    Keywords: Primary 03B45, 06E25 ; Secondary 18C10
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Philosophy
    Notes: Abstract We show that (contrary to the parallel case of intuitionistic logic, see [7], [4]) there does not exist a translation fromS42 (the propositional modal systemS4 enriched with propositional quantifiers) intoS4 that preserves provability and reduces to identity for Boolean connectives and □.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01061237
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  • 7
    Electronic Resource
    Electronic Resource
    Algorithmic problems concerning first-order definability of modal formulas on the class of all finite frames (1995)
    Springer
    Studia logica 55 (1995), S. 421-448 
    Details
    ISSN: 1572-8730
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Philosophy
    Notes: Abstract The main result is that is no effective algorithmic answer to the question:how to recognize whether arbitrary modal formula has a first-order equivalent on the class of finite frames. Besides, two known problems are solved: it is proved algorithmic undecidability of finite frame consequence between modal formulas; the difference between global and local variants of first-order definability of modal formulas on the class of transitive frames is shown.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01057806
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  • 8
    Electronic Resource
    Electronic Resource
    On variable separation in modal and superintuitionistic logics (1995)
    Springer
    Studia logica 55 (1995), S. 99-112 
    Details
    ISSN: 1572-8730
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Philosophy
    Notes: Abstract In this paper we find an algebraic equivalent of the Hallden property in modal logics, namely, we prove that the Hallden-completeness in any normal modal logic is equivalent to the so-called super-embedding property of a suitable class of modal algebras. The joint embedding property of a class of algebras is equivalent to the Pseudo-Relevance Property. We consider connections of the above-mentioned properties with interpolation and amalgamation. Also an algebraic equivalent of of the principle of variable separation in superintuitionistic logics will be found.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01053034
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  • 9
    Electronic Resource
    Electronic Resource
    The abstract variable-binding calculus (1995)
    Springer
    Studia logica 55 (1995), S. 129-179 
    Details
    ISSN: 1572-8730
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Philosophy
    Notes: Abstract Theabstract variable binding calculus (VB-calculus) provides a formal frame-work encompassing such diverse variable-binding phenomena as lambda abstraction, Riemann integration, existential and universal quantification (in both classical and nonclassical logic), and various notions of generalized quantification that have been studied in abstract model theory. All axioms of the VB-calculus are in the form of equations, but like the lambda calculus it is not a true equational theory since substitution of terms for variables is restricted. A similar problem with the standard formalism of the first-order predicate logic led to the development of the theory of cylindric and polyadic Boolean algebras. We take the same course here and introduce the variety of polyadic VB-algebras as a pure equational form of the VB-calculus. In one of the main results of the paper we show that every locally finite polyadic VB-algebra of infinite dimension is isomorphic to a functional polyadic VB-algebra that is obtained from a model of the VB-calculus by a natural coordinatization process. This theorem is a generalization of the functional representation theorem for polyadic Boolean algebras given by P. Halmos. As an application of this theorem we present a strong completeness theorem for the VB-calculus. More precisely, we prove that, for every VB-theory T that is obtained by adjoining new equations to the axioms of the VB-calculus, there exists a model D such that ⊢T s=t iff ⊨D s=t. This result specializes to a completeness theorem for a number of familiar systems that can be formalized as VB-calculi. For example, the lambda calculus, the classical first-order predicate calculus, the theory of the generalized quantifierexists uncountably many and a fragment of Riemann integration.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01053036
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  • 10
    Electronic Resource
    Electronic Resource
    Positive modal logic (1995)
    Springer
    Studia logica 55 (1995), S. 301-317 
    Details
    ISSN: 1572-8730
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Philosophy
    Notes: Abstract We give a set of postulates for the minimal normal modal logicK + without negation or any kind of implication. The connectives are simply ∧, ∨, □, ◊. The postulates (and theorems) are all deducibility statements ϕ ⊢ ψ. The only postulates that might not be obvious are $$\diamondsuit \varphi \wedge \square \psi \vdash \diamondsuit (\varphi \wedge \psi )\square (\varphi \vee \psi ) \vdash \square \varphi \vee \diamondsuit \psi $$ . It is shown thatK + is complete with respect to the usual Kripke-style semantics. The proof is by way of a Henkin-style construction, with “possible worlds” being taken to be prime theories. The construction has the somewhat unusual feature of using at an intermediate stage disjoint pairs consisting of a theory and a “counter-theory”, the counter-theory replacing the role of negation in the standard construction. Extension to other modal logics is discussed, as well as a representation theorem for the corresponding modal algebras. We also discuss proof-theoretic arguments.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01061239
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  • 11
    Electronic Resource
    Electronic Resource
    From the editors (1996)
    Springer
    Studia logica 57 (1996), S. 3-4 
    Details
    ISSN: 1572-8730
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Philosophy
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00370666
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  • 12
    Electronic Resource
    Electronic Resource
    Two approaches to the formalisation of defeasible deontic reasoning (1996)
    Springer
    Studia logica 57 (1996), S. 73-90 
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    ISSN: 1572-8730
    Keywords: deontic reasoning ; defeasible reasoning ; moral dilemmas
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Philosophy
    Notes: Abstract This paper compares two ways of formalising defeasible deontic reasoning, both based on the view that the issues of conflicting obligations and moral dilemmas should be dealt with from the perspective of nonmonotonic reasoning. The first way is developing a special nonmonotonic logic for deontic statements. This method turns out to have some limitations, for which reason another approach is recommended, viz. combining an already existing nonmonotonic logic with a deontic logic. As an example of this method the language of Reiter's default logic is extended to include modal expressions, after which the argumentation framework in default logic of [20, 22] is used to give a plausible logical analysis of moral dilemmas and prima facie obligations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00370670
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  • 13
    Electronic Resource
    Electronic Resource
    Deontic database constraints, violation and recovery (1996)
    Springer
    Studia logica 57 (1996), S. 139-165 
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    ISSN: 1572-8730
    Keywords: deontic logic ; database integrity ; constraints ; constraint violation ; recovery
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Philosophy
    Notes: Abstract The paper discusses the potential value of a deontic approach to database specification. More specifically, some different types of integrity constraints are considered and a distinction is drawn between necessary (“hard”) and deontic (“soft”) constraints. Databases are compared with other normative systems. A deontic logic for database specification is proposed and the problems of how to react to, and of how to correct, or repair, a situation which arises through norm violation are discussed in the context of this logic. The limitations of the proposed logic and possible modifications and extensions of it are analysed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00370673
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  • 14
    Electronic Resource
    Electronic Resource
    Doing well enough: Toward a logic for common-sense morality (1996)
    Springer
    Studia logica 57 (1996), S. 167-192 
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    ISSN: 1572-8730
    Keywords: deontic logic ; supererogation ; ordering semantics ; indifference ; optimality
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Philosophy
    Notes: Abstract On the traditional deontic framework, what is required (what morality demands) and what is optimal (what morality recommends) can't be distinguished and hence they can't both be represented. Although the morally optional can be represented, the supererogatory (exceeding morality's demands), one of its proper subclasses, cannot be. The morally indifferent, another proper subclass of the optional-one obviously disjoint from the supererogatory-is also not representable. Ditto for the permissibly suboptimal and the morally significant. Finally, the minimum that morality allows finds no place in the traditional scheme. With a focus on the question, “What would constitute a hospitable logical neighborhood for the concept of supererogation?”, I present and motivate an enriched logical and semantic framework for representing all these concepts of common sense morality.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00370674
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  • 15
    Electronic Resource
    Electronic Resource
    The finite model property for BCI and related systems (1996)
    Springer
    Studia logica 57 (1996), S. 303-323 
    Details
    ISSN: 1572-8730
    Keywords: finite models ; substructural logics ; the Lambek calculus ; 03B40 ; 03B60
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Philosophy
    Notes: Abstract We prove the finite model property (fmp) for BCI and BCI with additive conjunction, which answers some open questions in Meyer and Ono [11]. We also obtain similar results for some restricted versions of these systems in the style of the Lambek calculus [10, 3]. The key tool is the method of barriers which was earlier introduced by the author to prove fmp for the product-free Lambek calculus [2] and the commutative product-free Lambek calculus [4].
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00370837
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  • 16
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    Equivalential and algebraizable logics (1996)
    Springer
    Studia logica 57 (1996), S. 419-436 
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    ISSN: 1572-8730
    Keywords: algebraizable logics ; equivalential logics ; implicative logics ; protoalgebraic logics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Philosophy
    Notes: Abstract The notion of an algebraizable logic in the sense of Blok and Pigozzi [3] is generalized to that of a possibly infinitely algebraizable, for short, p.i.-algebraizable logic by admitting infinite sets of equivalence formulas and defining equations. An example of the new class is given. Many ideas of this paper have been present in [3] and [4]. By a consequent matrix semantics approach the theory of algebraizable and p.i.-algebraizable logics is developed in a different way. It is related to the theory of equivalential logics in the sense of Prucnal and Wroński [18], and it is extended to nonfinitary logics. The main result states that a logic is algebraizable (p.i.-algebraizable) iff it is finitely equivalential (equivalential) and the truth predicate in the reduced matrix models is equationally definable.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00370843
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  • 17
    Electronic Resource
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    A Completeness Proof for a Logic with an Alternative Necessity Operator (1997)
    Springer
    Studia logica 58 (1997), S. 99-112 
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    ISSN: 1572-8730
    Keywords: knowledge logic ; contingency ; completeness ; complexity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Philosophy
    Notes: Abstract We show the completeness of a Hilbert-style system LK defined by M. Valiev involving the knowledge operator K dedicated to the reasoning with incomplete information. The completeness proof uses a variant of Makinson's canonical model construction. Furthermore we prove that the theoremhood problem for LK is co-NP-complete, using techniques similar to those used to prove that the satisfiability problem for propositional S5 is NP-complete.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1004944015811
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  • 18
    Electronic Resource
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    A Logic for Information Systems (1997)
    Springer
    Studia logica 58 (1997), S. 3-16 
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    ISSN: 1572-8730
    Keywords: modal logic ; information system ; complete calculus
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Philosophy
    Notes: Abstract A conception of an information system has been introduced by Pawlak. The study has been continued in works of Pawlak and Orlowska and in works of Vakarelov. They had proposed some basic relations and had constructed a formal system of a modal logic that describes the relations and some of their Boolean combinations. Our work is devoted to a generalization of this approach. A class of relation systems and a complete calculus construction method for these systems are proposed. As a corollary of our main result, our paper contains a solution of a Vakarelov's problem: how to construct a formal system that describes all the Boolean combinations of the basic relations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1004927613994
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  • 19
    Electronic Resource
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    Fuzzy Logic and Arithmetical Hierarchy, II (1997)
    Springer
    Studia logica 58 (1997), S. 129-141 
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    ISSN: 1572-8730
    Keywords: fuzzy logic ; many-valued logic ; undecidability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Philosophy
    Notes: Abstract A very simple many-valued predicate calculus is presented; a completeness theorem is proved and the arithmetical complexity of some notions concerning provability is determined.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1004948116720
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  • 20
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    Towards a Rough Mereology-Based Logic for Approximate Solution Synthesis. Part 1 (1997)
    Springer
    Studia logica 58 (1997), S. 143-184 
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    ISSN: 1572-8730
    Keywords: approximate reasoning ; synthesis of complex objects ; rough sets ; mereology ; rough mereology
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Philosophy
    Notes: Abstract We are concerned with formal models of reasoning under uncertainty. Many approaches to this problem are known in the literature e.g. Dempster-Shafer theory [29], [42], bayesian-based reasoning [21], [29], belief networks [29], many-valued logics and fuzzy logics [6], non-monotonic logics [29], neural network logics [14]. We propose rough mereology developed by the last two authors [22-25] as a foundation for approximate reasoning about complex objects. Our notion of a complex object includes, among others, proofs understood as schemes constructed in order to support within our knowledge assertions/hypotheses about reality described by our knowledge incompletely.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1004900200790
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  • 21
    Electronic Resource
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    Axiomatising first-order temporal logic: Until and since over linear time (1996)
    Springer
    Studia logica 57 (1996), S. 279-302 
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    ISSN: 1572-8730
    Keywords: temporal logic ; axiomatization ; first-order temporal/modal logics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Philosophy
    Notes: Abstract We present an axiomatisation for the first-order temporal logic with connectives Until and Since over the class of all linear flows of time. Completeness of the axiom system is proved. We also add a few axioms to find a sound and complete axiomatisation for the first order temporal logic of Until and Since over rational numbers time.
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    URL: http://dx.doi.org/10.1007/BF00370836
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  • 22
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    Game logic and its applications I (1996)
    Springer
    Studia logica 57 (1996), S. 325-354 
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    ISSN: 1572-8730
    Keywords: infinitary predicate KD4 ; common knowledge ; Nash equilibrium ; undecidability on playability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Philosophy
    Notes: Abstract This paper provides a logic framework for investigations of game theoretical problems. We adopt an infinitary extension of classical predicate logic as the base logic of the framework. The reason for an infinitary extension is to express the common knowledge concept explicitly. Depending upon the choice of axioms on the knowledge operators, there is a hierarchy of logics. The limit case is an infinitary predicate extension of modal propositional logic KD4, and is of special interest in applications. In Part I, we develop the basic framework, and show some applications: an epistemic axiomatization of Nash equilibrium and formal undecidability on the playability of a game. To show the formal undecidability, we use a term existence theorem, which will be proved in Part II.
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    URL: http://dx.doi.org/10.1007/BF00370838
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  • 23
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    Helena Rasiowa in memoriam (1996)
    Springer
    Studia logica 57 (1996), S. 459-459 
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    ISSN: 1572-8730
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Philosophy
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00370845
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  • 24
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    An Elementary Proof of Chang's Completeness Theorem for the Infinite-valued Calculus of Lukasiewicz (1997)
    Springer
    Studia logica 58 (1997), S. 79-97 
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    ISSN: 1572-8730
    Keywords: MV algebra ; completeness of the Lukasiewicz calculus ; infinite-valued logic
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Philosophy
    Notes: Abstract The interpretation of propositions in Lukasiewicz's infinite-valued calculus as answers in Ulam's game with lies--the Boolean case corresponding to the traditional Twenty Questions game--gives added interest to the completeness theorem. The literature contains several different proofs, but they invariably require technical prerequisites from such areas as model-theory, algebraic geometry, or the theory of ordered groups. The aim of this paper is to provide a self-contained proof, only requiring the rudiments of algebra and convexity in finite-dimensional vector spaces.
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    URL: http://dx.doi.org/10.1023/A:1004991931741
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  • 25
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    Simulation and Transfer Results in Modal Logic – A Survey (1997)
    Springer
    Studia logica 59 (1997), S. 149-177 
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    ISSN: 1572-8730
    Keywords: modal logic ; transfer ; interpretation ; tense logic ; intuitionistic logic
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Philosophy
    Notes: Abstract This papers gives a survey of recent results about simulations of one class of modal logics by another class and of the transfer of properties of modal logics under extensions of the underlying modal language. We discuss: the transfer from normal polymodal logics to their fusions, the transfer from normal modal logics to their extensions by adding the universal modality, and the transfer from normal monomodal logics to minimal tense extensions. Likewise, we discuss simulations of normal polymodal logics by normal monomodal logics, of nominals and the difference operator by normal operators, of monotonic monomodal logics by normal bimodal logics, of polyadic normal modal logics by polymodal normal modal logics, and of intuitionistic modal logics by normal bimodal logics.
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    URL: http://dx.doi.org/10.1023/A:1004900300438
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  • 26
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    Knowledge on Treelike Spaces (1997)
    Springer
    Studia logica 59 (1997), S. 271-301 
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    ISSN: 1572-8730
    Keywords: bimodal logics ; logics of knowledge ; branching time ; persistence ; convexity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Philosophy
    Notes: Abstract This paper presents a bimodal logic for reasoning about knowledge during knowledge acquisitions. One of the modalities represents (effort during) non-deterministic time and the other represents knowledge. The semantics of this logic are tree-like spaces which are a generalization of semantics used for modeling branching time and historical necessity. A finite system of axiom schemes is shown to be canonically complete for the formentioned spaces. A characterization of the satisfaction relation implies the small model property and decidability for this system.
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    URL: http://dx.doi.org/10.1023/A:1004908502255
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  • 27
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    Strategic Construction of Fitch-style Proofs (1998)
    Springer
    Studia logica 60 (1998), S. 45-66 
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    ISSN: 1572-8730
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Philosophy
    Notes: Abstract Symlog is a system for learning symbolic logic by computer that allows students to interactively construct proofs in Fitch-style natural deduction. On request, Symlog can provide guidance and advice to help a student narrow the gap between goal theorem and premises. To effectively implement this capability, the program was equipped with a theorem prover that constructs proofs using the same methods and techniques the students are being taught. This paper discusses some of the aspects of the theorem prover's design, including its set of proof-construction strategies, its unification algorithm as well as some of the tradeoffs between efficiency and pedagogy.
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    URL: http://dx.doi.org/10.1023/A:1005087316935
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  • 28
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    Lambda Calculus and Intuitionistic Linear Logic (1997)
    Springer
    Studia logica 59 (1997), S. 417-448 
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    ISSN: 1572-8730
    Keywords: linear logic ; Curry-Howard isomorphism ; typed λ-calculi
    Source: Springer Online Journal Archives 1860-2000
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    Notes: Abstract The introduction of Linear Logic extends the Curry-Howard Isomorphism to intensional aspects of the typed functional programming. In particular, every formula of Linear Logic tells whether the term it is a type for, can be either erased/duplicated or not, during a computation. So, Linear Logic can be seen as a model of a computational environment with an explicit control about the management of resources. This paper introduces a typed functional language Λ! and a categorical model for it. The terms of Λ! encode a version of natural deduction for Intuitionistic Linear Logic such that linear and non linear assumptions are managed multiplicatively and additively, respectively. Correspondingly, the terms of Λ! are built out of two disjoint sets of variables. Moreover, the λ-abstractions of Λ! bind variables and patterns. The use of two different kinds of variables and the patterns allow a very compact definition of the one-step operational semantics of Λ!, unlike all other extensions of Curry-Howard Isomorphism to Intuitionistic Linear Logic. The language Λ! is Church-Rosser and enjoys both Strong Normalizability and Subject Reduction. The categorical model induces operational equivalences like, for example, a set of extensional equivalences. The paper presents also an untyped version of Λ! and a type assignment for it, using formulas of Linear Logic as types. The type assignment inherits from Λ! all the good computational properties and enjoys also the Principal-Type Property.
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    Linear Lambda-Terms and Natural Deduction (1998)
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    Studia logica 60 (1998), S. 209-231 
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    Elementary Extensions of External Classes in a Nonstandard Universe (1998)
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    Studia logica 60 (1998), S. 253-273 
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    Keywords: nonstandard set theory ; inner subuniverses ; constructibility ; iterated elementary extensions
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    Notes: Abstract In continuation of our study of HST, Hrbaček set theory (a nonstandard set theory which includes, in particular, the ZFC Replacement and Separation schemata in the st-∈-language, and Saturation for well-orderable families of internal sets), we consider the problem of existence of elementary extensions of inner "external" subclasses of the HST universe. We show that, given a standard cardinal κ, any set R ⊑ *κ generates an "internal" class S(R) of all sets standard relatively to elements of R, and an "external" class L[S(R)] of all sets constructible (in a sense close to the Gödel constructibility) from sets in S(R). We prove that under some mild saturation-like requirements for R the class L[S(R)] models a certain κ-version of HST including the principle of κ+-saturation; moreover, in this case L[S(R′)] is an elementary extension of L[S(R)] in the st-∈-language whenever sets R ⊑ R′ satisfy the requirements.
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    Preservation Theorems Without Continuum Hypothesis (1998)
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    Studia logica 60 (1998), S. 343-355 
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    Keywords: Horn sentence ; reduced product ; reduced power ; ultrapower ; and ultraproduct
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    Notes: Abstract Many results concerning the equivalence between a syntactic form of formulas and a model theoretic conditions are proven directly without using any form of a continuum hypothesis. In particular, it is demonstrated that any reduced product sentence is equivalent to a Horn sentence. Moreover, in any first order language without equality one now has that a reduced product sentence is equivalent to a Horn sentence and any sentence is equivalent to a Boolean combination of Horn sentences.
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    Characterizations of Negative Definability in Modal Logic (1998)
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    Studia logica 60 (1998), S. 357-386 
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    Keywords: Modal logic ; definability ; irreflexivity rule ; characterization
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    Notes: Abstract Negative definability ([18]) is an alternative way of defining classes of Kripke frames via a modal language, one that enables us, for instance, to define the class of irreflexive frames. Besides a list of closure conditions for negatively definable classes, the paper contains two main theorems. First, a characterization is given of negatively definable classes of (rooted) finite transitive Kripke frames and of such classes defined using both traditional (positive) and negative definitions. Second, we characterize the negatively definable classes of rooted general frames.
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    The Writing of the MV-algebras (1998)
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    Studia logica 61 (1998), S. 3-6 
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    Books Received: Jürgen Mittelstrass, Enzyklopädie Philosophie und Wissenschaftstheorie (1998)
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    Studia logica 60 (1998), S. 441-448 
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    Connections Between BCK-algebras and Difference Posetse (1998)
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    Studia logica 60 (1998), S. 421-439 
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    Keywords: BCK-algebra ; commutative BCK-algebra ; poset with difference ; D-poset ; MV-algebra ; quantum MV-algebra ; orthoalgebra
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    Notes: Abstract We discuss the interrelations between BCK-algebras and posets with difference. Applications are given to bounded commutative BCK-algebras, difference posets, MV-algebras, quantum MV-algebras and orthoalgebras.
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    Commodious Axiomatization of Quantifiers in Multiple-Valued Logic (1998)
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    Studia logica 61 (1998), S. 101-121 
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    Keywords: many-valued logic ; infinitely-valued logic ; distribution quantifiers ; distributive lattices ; semantic tableaux ; sequent calculi
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    Notes: Abstract We provide tools for a concise axiomatization of a broad class of quantifiers in many-valued logic, so-called distribution quantifiers. Although sound and complete axiomatizations for such quantifiers exist, their size renders them virtually useless for practical purposes. We show that for quantifiers based on finite distributive lattices compact axiomatizations can be obtained schematically. This is achieved by providing a link between skolemized signed formulas and filters/ideals in Boolean set lattices. Then lattice theoretic tools such as Birkhoff's representation theorem for finite distributive lattices are used to derive tableau-style axiomatizations of distribution quantifiers.
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    On Some Kripke Complete and Kripke Incomplete Intermediate Predicate Logics (1998)
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    Studia logica 61 (1998), S. 281-292 
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    Notes: Abstract The Kripke-completeness and incompleteness of some intermediate predicate logics is established. In particular, we obtain a Kripke-incomplete logic (H* +A+D+K) where H* is the intuitionistic predicate calculus, A is a disjunction-free propositional formula, D = ∀x(P(x) V Q) ⊃ ∀xP(x) V Q, K = ¬¬∀x(P(x) V ¬P(x)) (the negative answer to a question of T. Shimura).
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    Subdirectly Irreducible Modal Algebras and Initial Frames (1999)
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    Studia logica 62 (1999), S. 269-282 
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    Keywords: duality theory in modal logic ; modal algebras ; generated frames ; subdirect irreducibility
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    Notes: Abstract The duality between general frames and modal algebras allows to transfer a problem about the relational (Kripke) semantics into algebraic terms, and conversely. We here deal with the conjecture: the modal algebra A is subdirectly irreducible (s.i.) if and only if the dual frame A* is generated. We show that it is false in general, and that it becomes true under some mild assumptions, which include the finite case and the case of K4. We also prove that a Kripke frame F is generated if and only if the dual algebra F* is s.i. The technical result is that A is s.i. when the set of points which generate the dual frame A* is not of zero measure.
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    Monotone Majorizable Functionals (1999)
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    Studia logica 62 (1999), S. 283-289 
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    Keywords: Monotone functionals ; monotone majorizable functionals ; hereditarily majorizable functionals ; simply typed lambda-calculus ; extensionality ; Dialectica interpretation
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    Notes: Abstract Several properties of monotone functionals (MF) and monotone majorizable functionals (MMF) used in the earlier work by the author and van de Pol are proved. It turns out that the terms of the simply typed lambda-calculus define MF, but adding primitive recursion, and even monotonic primitive recursion changes the situation: already λZ.Z(1 — sg) is not MMF. It is proved that extensionality is not Dialectica-realizable by MMF, and a simple example of a MF which is not hereditarily majorizable is given.
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    From Brouwerian Counter Examples to the Creating Subject (1999)
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    Studia logica 62 (1999), S. 305-314 
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    Keywords: intuitionism ; Brouwerian counter examples ; continuum ; creating subject
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    Notes: Abstract The original Brouwerian counter examples were algorithmic in nature; after the introduction of choice sequences, Brouwer devised a version which did not depend on algorithms. This is the origin of the ‘creating subject’ technique. The method allowed stronger refutations of classical principles. Here it is used to show that ‘negative dense’ subsets of the continuum are indecomposable.
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    Preface (1999)
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    Studia logica 62 (1999), S. 117-120 
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    Marginalia on Sequent Calculi (1999)
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    Studia logica 62 (1999), S. 291-303 
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    Keywords: sequent calculus ; normal deduction ; cutfree deduction ; complete discharge convention
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    Notes: Abstract The paper discusses the relationship between normal natural deductions and cutfree proofs in Gentzen (sequent) calculi in the absence of term labeling. For Gentzen calculi this is the usual version; for natural deduction this is the version under the complete discharge convention, where open assumptions are always discharged as soon as possible. The paper supplements work by Mints, Pinto, Dyckhoff, and Schwichtenberg on the labeled calculi.
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    A Translation of Intuitionistic Predicate Logic into Basic Predicate Logic (1999)
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    Studia logica 62 (1999), S. 341-352 
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    Keywords: Basic Predicate Logic ; Intuitionistic Predicate Logic ; translation
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    Notes: Abstract Basic Predicate Logic, BQC, is a proper subsystem of Intuitionistic Predicate Logic, IQC. For every formula ϕ in the language {∨, ∧, →, ⊤, ⊥, ∀, ∃}, we associate two sequences of formulas 〈ϕ0,ϕ1,...〉 and 〈ϕ0,ϕ1,...〉 in the same language. We prove that for every sequent ϕ ⇒ ψ, there are natural numbers m, n, such that IQC ⊢ ϕ ⇒ ψ, iff BQC ⊢ ϕn ⇒ ψm. Some applications of this translation are mentioned.
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    Conservative Theories of Classical Truth (1999)
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    Studia logica 62 (1999), S. 353-370 
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    Keywords: truth ; satisfaction class ; cut elimination
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    Notes: Abstract Some axiomatic theories of truth and related subsystems of second-order arithmetic are surveyed and shown to be conservative over their respective base theory. In particular, it is shown by purely finitistically means that the theory PA ÷ "there is a satisfaction class" and the theory FS↾ of [2] are conservative over PA.
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    Quantifiers and Congruence Closure (1999)
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    Studia logica 62 (1999), S. 315-340 
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    Keywords: generalized quantifier ; finite model theory
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    Notes: Abstract We prove some results about the limitations of the expressive power of quantifiers on finite structures. We define the concept of a bounded quantifier and prove that every relativizing quantifier which is bounded is already first-order definable (Theorem 3.8). We weaken the concept of congruence closed (see [6]) to weakly congruence closed by restricting to congruence relations where all classes have the same size. Adapting the concept of a thin quantifier (Caicedo [1]) to the framework of finite structures, we define the concept of a meager quantifier. We show that no proper extension of first-order logic by means of meager quantifiers is weakly congruence closed (Theorem 4.9). We prove the failure of the full congruence closure property for logics which extend first-order logic by means of meager quantifiers, arbitrary monadic quantifiers, and the Härtig quantifier (Theorem 6.1).
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    Minimal p-morphic Images, Axiomatizations and Coverings in the Modal Logic K4 (1999)
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    Studia logica 62 (1999), S. 371-398 
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    Keywords: Kripke frames ; p-morphisms ; axiomatizations ; covers
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    Notes: Abstract We define the concepts of minimal p-morphic image and basic p-morphism for transitive Kripke frames. These concepts are used to determine effectively the least number of variables necessary to axiomatize a tabular extension of K4, and to describe the covers and co-covers of such a logic in the lattice of the extensions of K4.
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    Book Reviews (1999)
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    Studia logica 62 (1999), S. 429-448 
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    Contents of Volume 62 (1999)
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    Studia logica 62 (1999), S. 449-451 
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    Proof-Theoretic Modal PA-Completeness I: A System-Sequent Metric (1999)
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    Studia logica 63 (1999), S. 27-48 
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    Keywords: Proof-Theory ; Probability Logic ; metric between sentences and systems ; characteristic formula of a modal sequent
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    Notes: Abstract This paper is the first of a series of three articles that present the syntactic proof of the PA-completeness of the modal system G, by introducing suitable proof-theoretic objects, which also have an independent interest. We start from the syntactic PA-completeness of modal system GL-LIN, previously obtained in [7], [8], and so we assume to be working on modal sequents S which are GL-LIN-theorems. If S is not a G-theorem we define here a notion of syntactic metric d(S, G): we calculate a canonical characteristic fomula H of S (char(S)) so that ⊢G ∼ H → (∼S) and ⊢GL-LIN ∼ H, and the complexity σ of ∼ H gives the distance d(S, G) of S from G. Then, in order to produce the whole completeness proof as an induction on this d(S, G), we introduce the tree-interpretation of a modal sequent Q into PA, that sends the letters of Q into PA-formulas describing the properties of a GL-LIN-proof P of Q: It is also a d(*, G)-metric linked interpretation, since it will be applied to a proof-tree T of ∼ H with H = char(S) and σ(∼ H) = d(S, G).
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    Some Logics of Iterated Belief Change (1999)
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    Studia logica 63 (1999), S. 49-84 
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    Notes: Abstract The problems that surround iterated contractions and expansions of beliefs are approached by studying hypertheories, a generalisation of Adam Grove's notion of systems of spheres. By using a language with dynamic and doxastic operators different ideas about the basic nature of belief change are axiomatised. It is shown that by imposing quite natural constraints on how hypertheories may change, the basic logics for belief change can be strengthened considerably to bring one closer to a theory of iterated belief change. It is then argued that the logic of expansion, in particular, cannot without loss of generality be strengthened any further to allow for a full logic of iterated belief change. To remedy this situation a notion of directed expansion is introduced that allows for a full logic of iterated belief change. The new operation is given an axiomatisation that is complete for linear hypertheories.
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    New Intuitionistic Logical Constants and Novikov Completeness (1999)
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    Studia logica 63 (1999), S. 151-180 
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    Keywords: intuitionistic logic ; new logical constants ; Novikov completeness
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    Notes: Abstract Extending the language of the intuitionistic propositional logic Int with additional logical constants, we construct a wide family of extensions of Int with the following properties: (a) every member of this family is a maximal conservative extension of Int; (b) additional constants are independent in each of them.
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    Substructural Implicational Logics Including the Relevant Logic E (1999)
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    Studia logica 63 (1999), S. 181-212 
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    Keywords: substructural logic ; relevant logic ; cut-elimination
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    Notes: Abstract We introduce several restricted versions of the structural rules in the implicational fragment of Gentzen's sequent calculus LJ. For example, we permit the applications of a structural rule only if its principal formula is an implication. We investigate cut-eliminability and theorem-equivalence among various combinations of them. The results include new cut-elimination theorems for the implicational fragments of the following logics: relevant logic E, strict implication S4, and their neighbors (e.g., E-W and S4-W); BCI-logic, BCK-logic, relevant logic R, and the intuitionistic logic.
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    Proof-Theoretic Modal PA-Completeness II: The Syntactic Countermodel (1999)
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    Studia logica 63 (1999), S. 245-268 
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    Keywords: Proof-Theory ; Provability Logic ; countermodel of a sequent ; classification of arithmetical interpretations of modal logic
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    Notes: Abstract This paper is the second part of the syntactic demonstration of the Arithmetical Completeness of the modal system G, the first part of which is presented in [9]. Given a sequent S so that ⊢GL-LIN S, ⊬G S, and given its characteristic formula H = char(S), which expresses the non G-provability of S, we construct a canonical proof-tree T of ~ H in GL-LIN, the height of which is the distance d(S, G) of S from G. T is the syntactic countermodel of S with respect to Gand is a tool of general interest in Provability Logic, that allows some classification in the set of the arithmetical interpretations.
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    L. T. F. Gamut, Logic, Language, and Information, Volume 1: Introduction to Logic; L. T. F. Gamut, Logic, Language, and Information, Volume 2: Intensional Logic and Logical Grammar (1999)
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    Studia logica 63 (1999), S. 269-300 
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    Basic Logic, K4, and Persistence (1999)
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    Studia logica 63 (1999), S. 343-352 
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    Keywords: Basic Logic ; Bisimulation ; Kripke Model ; Persistence
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    Notes: Abstract We characterize the first-order formulas with one free variable that are preserved under bisimulation and persistence or strong persistence over the class of Kripke models with transitive frames and unary persistent predicates.
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    Actuality and World-Indexed Sentences (1999)
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    Studia logica 63 (1999), S. 311-330 
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    Keywords: modal logic ; actuality indexed sentences
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    Notes: Abstract Some logical properties of modal languages in which actuality is expressible are investigated. It is argued that, if a sentence like 'Actually, Quine is a distinguished philosopher' is understood as a special case of world-indexed sentences (the index being the actual world), then actuality can be expressed only under strong modal assumptions. Some rival rigid and indexical approaches to actuality are discussed.
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    Selective Revision (1999)
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    Studia logica 63 (1999), S. 331-342 
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    Keywords: belief change ; belief revision ; success postulate ; non-prioritized revision ; choice function
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    Notes: Abstract We introduce a constructive model of selective belief revision in which it is possible to accept only a part of the input information. A selective revision operator ο is defined by the equality K ο α = K * f(α), where * is an AGM revision operator and f a function, typically with the property ⊢ α → f(α). Axiomatic characterizations are provided for three variants of selective revision.
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    Proof-Theoretic Modal PA-Completeness III: The Syntactic Proof (1999)
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    Studia logica 63 (1999), S. 301-310 
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    Keywords: Proof-Theory ; Provability Logic ; metric between sentences and systems ; PA-representation of the syntactic countrmodel of a modal sequent.
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    Notes: Abstract This paper is the final part of the syntactic demonstration of the Arithmetical Completeness of the modal system G; in the preceding parts [9] and [10] the tools for the proof were defined, in particular the notion of syntactic countermodel. Our strategy is: PA-completeness of G as a search for interpretations which force the distance between G and a GL-LIN-theorem to zero. If the GL-LIN-theorem S is not a G-theorem, we construct a formula H expressing the non G-provability of S, so that ⊢GL-LIN ∼ H and so that a canonical proof T of ∼ H in GL-LIN is a syntactic countermodel for S with respect to G, which has the height θ(T) equal to the distance d(S, G) of S from G. Then we define the interpretation ξ of S which represents the proof-tree T in PA. By induction on θ(T), we prove that ⊢PA Sξ and d(S, G) 〉 0 imply the inconsistency of PA.
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    Book Reviews (1999)
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    Studia logica 63 (1999), S. 417-448 
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    On Canonicity and Strong Completeness Conditions in Intermediate Propositional Logics (1999)
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    Studia logica 63 (1999), S. 353-385 
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    Keywords: strong completeness ; strong w-completeness ; completeness ; hypercanonicity ; extensive canonicity ; canonicity ; extensive w-canonicity ; w-canonicity
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    Notes: Abstract By using algebraic-categorical tools, we establish four criteria in order to disprove canonicity, strong completeness, w-canonicity and strong w-completeness, respectively, of an intermediate propositional logic. We then apply the second criterion in order to get the following result: all the logics defined by extra-intuitionistic one-variable schemata, except four of them, are not strongly complete. We also apply the fourth criterion in order to prove that the Gabbay-de Jongh logic D1 is not strongly w-complete.
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    Algebraic Kripke Sheaf Semantics for Non-Classical Predicate Logics (1999)
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    Studia logica 63 (1999), S. 387-416 
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    Keywords: super-intuitionistic predicate logics ; modal predicate logics ; Kripke semantics ; algebraic semantics ; disjunction property ; existence property
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    Notes: Abstract In so-called Kripke-type models, each sentence is assigned either to true or to false at each possible world. In this setting, every possible world has the two-valued Boolean algebra as the set of truth values. Instead, we take a collection of algebras each of which is attached to a world as the set of truth values at the world, and obtain an extended semantics based on the traditional Kripke-type semantics, which we call here the algebraic Kripke semantics. We introduce algebraic Kripke sheaf semantics for super-intuitionistic and modal predicate logics, and discuss some basic properties. We can state the Gödel-McKinsey-Tarski translation theorem within this semantics. Further, we show new results on super-intuitionistic predicate logics. We prove that there exists a continuum of super-intuitionistic predicate logics each of which has both of the disjunction and existence properties and moreover the same propositional fragment as the intuitionistic logic.
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    A note on the proof theory the λII-calculus (1995)
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    Studia logica 54 (1995), S. 199-230 
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    Notes: Abstract The λII-calculus, a theory of first-order dependent function types in Curry-Howard-de Bruijn correspondence with a fragment of minimal first-order logic, is defined as a system of (linearized) natural deduction. In this paper, we present a Gentzen-style sequent calculus for the λII-calculus and prove the cut-elimination theorem. The cut-elimination result builds upon the existence of normal forms for the natural deduction system and can be considered to be analogous to a proof provided by Prawitz for first-order logic. The type-theoretic setting considered here elegantly illustrates the distinction between the processes of normalization in a natural deduction system and cut-elimination in a Gentzen-style sequent calculus. We consider an application of the cut-free calculus, via the subformula property, to proof-search in the λII-calculus. For this application, the normalization result for the natural deduction calculus alone is inadequate, a (cut-free) calculus with the subformula property being required.
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    Connectification forn-contraction (1995)
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    Studia logica 54 (1995), S. 149-171 
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    Notes: Abstract In this paper, we introduce connectification operators for intuitionistic and classical linear algebras corresponding to linear logic and to some of its extensions withn-contraction. In particular,n-contraction (n≥2) is a version of the contraction rule, wheren+1 occurrences of a formula may be contracted ton occurrences. Since cut cannot be eliminated from the systems withn-contraction considered most of the standard proof-theoretic techniques to investigate meta-properties of those systems are useless. However, by means of connectification we establish the disjunction property for both intuitionistic and classical affine linear logics withn-contraction.
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    Discursive logic towards a logic of rational discourse (1995)
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    Studia logica 54 (1995), S. 231-249 
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    Notes: Abstract Both logic and philosophy of science investigate formal aspects of scientific discourse, i.e. properties of (non-monotonic) consequence operations for discursive logic. In the present paper we handle two of them: paraconsistency and enthymematycity.
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    A partially ordered extention of the integers (1995)
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    Studia logica 54 (1995), S. 303-332 
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    Notes: Abstract This paper presents a monotonic system of Post algebras of order ω+ω* whose chain of Post constans is isomorphic with 0≤1≤2≤ ... ≤-3≤-2≤-1. Besides monotonic operations, other unary operations are considered; namely, disjoint operations, the quasi-complement, succesor, and predecessor operations. The successor and predecessor operations are basic for number theory.
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    Busy choice sequences refraining formulas and modalities (1995)
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    Studia logica 54 (1995), S. 267-301 
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    Notes: Abstract The purpose of this paper is to present some results instit theory, a theory of agency proposed by N. Belnap and M. Perloff. We will establish a correspondence between the numbers ofstit modalities and the complexity degrees ofbusy choice sequences in semantic structures, and consequently, a correspondence between the number of modes of actions/inactions instit theory and the complexity degrees ofbusy choice sequences in semantic structures.
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    On Jaśkowski's discussive logics (1995)
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    Studia logica 54 (1995), S. 33-60 
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    Notes: Abstract We expose the main ideas, concepts and results about Jaśkowski's discussive logic, and apply that logic to the concept of pragmatic truth and to the Dalla Chiara-di Francia view of the foundations of physics.
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    On the predicate logics of finite Kripke frames (1995)
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    Studia logica 54 (1995), S. 79-88 
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    Notes: Abstract In [Ono 1987] H. Ono put the question about axiomatizing the intermediate predicate logicLFin characterized by the class of all finite Kripke frames (Problem 4,P41). It was established in [Skvortsov 1988] thatLFin is not recursively axiomatizable. One can easily show that for any finite posetM, the predicate logic characterized byM is recursively axiomatizable, and its axiomatization can be constructed effectively fromM. Namely, the set of formulas belonging to this logic is recursively enumerable, since it is embeddable in the two-sorted classical predicate calculusCPC 2 (the definition of the truth in a Kripke model may be expressed by a formula ofCPC 2). Thus the logicLFin is II 2 0 -arithmetical. Here we give a more explicit II 2 0 -description ofLFin: it is presented as the intersection of a denumerable sequence of finitely axiomatizable Kripke-complete logics. Namely, we give an axiomatization of the logicLB n P m + characterized by the class of all posets of the finite height ⩽m and the finite branching ⩽n. A finite axiomatization of the predicate logicLP m + characterized by the class of all posets of the height ⩽m is known from [Yokota 1989] (this axiomatics is essentially first-order; the standard propositional axiom of the height ⩽m is not sufficient [Ono 1983]). We prove thatLB n P m + =(LP m + +B n),B n being the propositional axiom of the branching ⩽n (see [Gabbay, de Jongh 1974]). Our terminology and notations mainly correspond to [Ono 1987].
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    Constructing a continuum of predicate extensions of each intermediate propositional logic (1995)
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    Studia logica 54 (1995), S. 173-198 
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    Notes: Abstract Wajsberg and Jankov provided us with methods of constructing a continuum of logics. However, their methods are not suitable for super-intuitionistic and modal predicate logics. The aim of this paper is to present simple ways of modification of their methods appropriate for such logics. We give some concrete applications as generic examples. Among others, we show that there is a continuum of logics (1) between the intuitionistic predicate logic and the logic of constant domains, (2) between a predicate extension ofS4 andS4 with the Barcan formula. Furthermore, we prove that (3) there is a continuum of predicate logics with equality whose “equality-free fragment” is just the intuitionistic predicate logic.
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    Editorial (1995)
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    Studia logica 55 (1995), S. 1-1 
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    Undecidability, incompleteness and Arnol'd problems (1995)
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    Studia logica 55 (1995), S. 23-32 
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    Notes: Abstract We present some recent technical results of us on the incompleteness of classical analysis and then discuss our work on the Arnol'd decision problems for the stability of fixed points of dynamical systems.
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    From the editors (1996)
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    Studia logica 56 (1996), S. 1-1 
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    Axiomatic extensions of the constructive logic with strong negation and the disjunction property (1995)
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    Studia logica 55 (1995), S. 377-388 
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    Notes: Abstract We study axiomatic extensions of the propositional constructive logic with strong negation having the disjunction property in terms of corresponding to them varieties of Nelson algebras. Any such varietyV is characterized by the property: (PQWC) ifA,B εV, thenA×B is a homomorphic image of some well-connected algebra ofV. We prove: each varietyV of Nelson algebras with PQWC lies in the fibre σ−1(W) for some varietyW of Heyting algebras having PQWC, for any varietyW of Heyting algebras with PQWC the least and the greatest varieties in σ−1(W) have PQWC, there exist varietiesW of Heyting algebras having PQWC such that σ−1(W) contains infinitely many varieties (of Nelson algebras) with PQWC.
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    Books received (1995)
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    Studia logica 55 (1995), S. 449-451 
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    Optimal natural dualities for varieties of Heyting algebras (1996)
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    Studia logica 56 (1996), S. 67-96 
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    Keywords: Heyting algebra ; natural duality ; optimal duality ; 06D20 ; 06D05 ; 08B99
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    Notes: Abstract The techniques of natural duality theory are applied to certain finitely generated varieties of Heyting algebras to obtain optimal dualities for these varieties, and thereby to address algebraic questions about them. In particular, a complete characterisation is given of the endodualisable finite subdirectly irreducible Heyting algebras. The procedures involved rely heavily on Priestley duality for Heyting algebras.
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    List of published papers (1996)
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    Studia logica 56 (1996), S. 277-290 
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    Announcement (1996)
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    Studia logica 56 (1996), S. 291-291 
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    Quantum MV algebras (1996)
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    Studia logica 56 (1996), S. 393-417 
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    Keywords: MV algebra ; Multi-valued logic ; quantum MV algebra ; unsharp orthoalgebra ; unsharp quantum mechanics
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    Notes: Abstract We introduce the notion of quantum MV algebra (QMV algebra) as a generalization of MV algebras and we show that the class of all effects of any Hilbert space gives rise to an example of such a structure. We investigate some properties of QMV algebras and we prove that QMV algebras represent non-idempotent extensions of orthomodular lattices.
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    Directions in generalized quantifier theory (1995)
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    Studia logica 55 (1995), S. 389-419 
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    Notes: Abstract We give a condensed survey of recent research on generalized quantifiers in logic, linguistics and computer science, under the following headings: Logical definability and expressive power, Polyadic quantifiers and linguistic definability, Weak semantics and axiomatizability, Computational semantics, Quantifiers in dynamic settings, Quantifiers and modal logic, Proof theory of generalized quantifiers.
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    The dual space of a finite simple Ockham algebra (1996)
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    Studia logica 56 (1996), S. 3-21 
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    Notes: Abstract Let (L; f) be a finite simple Ockham algebra and let (X;g) be its dual space. We first prove that every connected component of X is either a singleton or a generalised crown (i.e. an ordered set that is connected, has length 1, and all vertices of which have the same degree). The representation of a generalised crown by a square (0,1)-matrix in which all line sums are equal is used throughout, and a complete description of X, including the number of connected components and the degree of the vertices, is given. We then examine the converse problem of when a generalised crown can be made into a connected component of (X; g). We also determine the number of non-isomorphic finite simple Ockham algebras that belong properly to a given subvariety P 2n,0. Finally, we show that the number of fixed points of (L; f) is 0,1, or 2 according to the nature of X.
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    Representation of finite demi-p-lattices by means of posets (1996)
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    Studia logica 56 (1996), S. 97-110 
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    Keywords: demi-p-lattice ; almost-p-lattice ; free algebra ; duality ; poset
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    Notes: Abstract Finite demi-p-lattices are described in terms of the poset of its join irreducible elements endowed with a suitable set of maps. Description of the free algebras of demi-p-lattices and almost-p-lattices with n free generators are given.
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    A simplified duality for implicative lattices and l-groups (1996)
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    Studia logica 56 (1996), S. 185-204 
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    Keywords: duality ; Priestley spaces ; lattice-ordered groups ; implicative lattices
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    Notes: Abstract A topological duality is presented for a wide class of lattice-ordered structures including lattice-ordered groups. In this new approach, which simplifies considerably previous results of the author, the dual space is obtained by endowing the Priestley space of the underlying lattice with two binary functions, linked by set-theoretical complement and acting as symmetrical partners. In the particular case of l-groups, one of these functions is the usual product of sets and the axiomatization of the dual space is given by very simple first-order sentences, saying essentially that both functions are associative and that the space is a residuated semigroup with respect to each of them.
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    Reasoning about actions and obligations in first-order logic (1996)
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    Studia logica 57 (1996), S. 221-237 
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    Keywords: deontic logic ; logic of action
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    Notes: Abstract We describe a new way in which theories about the deontic status of actions can be represented in terms of the standard two-sorted first-order extensional predicate calculus. Some of the resulting formal theories are easy to implement in Prolog; one prototype implementation—R. M. Lee's deontic expert shell DX—is briefly described.
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    Definability of directly indecomposable congruence modular algebras (1996)
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    Studia logica 57 (1996), S. 239-241 
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    Keywords: congruence modular algebras ; directly indecomposable algebras ; central elements
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    Notes: Abstract It is proved that the directly indecomposable algebras in a congruence modular equational class ν form a ∀∃∀ first-order class provided that ν fulfils some two natural assumptions.
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    On maximal intermediate predicate constructive logics (1996)
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    Studia logica 57 (1996), S. 373-408 
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    Keywords: intermediate predicate logic ; nonstandard intermediate predicate logic ; predicate constructive logic ; nonstandard predicate constructive logic ; maximal predicate constructive logic ; maximal nonstandard predicate constructive logic ; smooth predicate constructive logic ; 03B55 ; 03C90
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    Notes: Abstract We extend to the predicate frame a previous characterization of the maximal intermediate propositional constructive logics. This provides a technique to get maximal intermediate predicate constructive logics starting from suitable sets of classically valid predicate formulae we call maximal nonstandard predicate constructive logics. As an example of this technique, we exhibit two maximal intermediate predicate constructive logics, yet leaving open the problem of stating whether the two logics are distinct. Further properties of these logics will be also investigated.
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    Generalized Rough Sets (Preclusivity Fuzzy-Intuitionistic (BZ) Lattices) (1997)
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    Studia logica 58 (1997), S. 47-77 
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    Keywords: Discernibility relations ; generalized rough sets ; Brouwer-Zadeh structures ; Fuzzy-intuitionistic algebras with modalities
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    Notes: Abstract The standard Pawlak approach to rough set theory, as an approximation space consisting of a universe U and an equivalence (“indiscernibility”) relation R $$ \subseteq$$ U x U, can be equivalently described by the induced preclusivity ("discernibility") relation U x U \ R, which is irreflexive and symmetric. We generalize the notion of approximation space as a pair consisting of a universe U and a discernibility or preclusivity (irreflexive and symmetric) relation, not necessarily induced from an equivalence relation. In this case the "elementary" sets are not mutually disjoint, but all the theory of generalized rough sets can be developed in analogy with the standard Pawlak approach. On the power set of the universe, the algebraic structure of the quasi fuzzy-intuitionistic "classical" (BZ) lattice is introduced and the sets of all "closed" and of all "open" definable sets with the associated complete (in general nondistributive) ortholattice structures are singled out. The rough approximation of any fixed subset of the universe is the pair consisting of the best "open" approximation from the bottom and the best "closed" approximation from the top. The properties of this generalized rough approximation mapping are studied in the context of quasi-BZ lattice structures of "closed-open" ordered pairs (the "algebraic logic" of generalized rough set theory), comparing the results with the standard Pawlak approach. A particular weak form of rough representation is also studied.
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    Consequence Operations Based on Hypergraph Satisfiability (1997)
    Springer
    Studia logica 58 (1997), S. 261-272 
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    ISSN: 1572-8730
    Keywords: hypergraph ; clause ; satisfiability ; consistency ; resolution ; compactness ; consequence operators
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Philosophy
    Notes: Abstract Four consequence operators based on hypergraph satisfiability are defined. Their properties are explored and interconnections are displayed. Finally their relation to the case of the Classical Propositional Calculus is shown.
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    URL: http://dx.doi.org/10.1023/A:1004923723916
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    A Logic for Reasoning about Relative Similarity (1997)
    Springer
    Studia logica 58 (1997), S. 185-226 
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    ISSN: 1572-8730
    Keywords: rough sets ; entities ; properties ; similarity ; lower and upper approximations ; multi-modal logics ; completeness
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Philosophy
    Notes: Abstract A similarity relation is a reflexive and symmetric binary relation between objects. Similarity is relative: it depends on the set of properties of objects used in determining their similarity or dissimilarity. A multi-modal logical language for reasoning about relative similarities is presented. The modalities correspond semantically to the upper and lower approximations of a set of objects by similarity relations corresponding to all subsets of a given set of properties of objects. A complete deduction system for the language is presented.
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    URL: http://dx.doi.org/10.1023/A:1004952317628
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    Game Logic and its Applications II (1997)
    Springer
    Studia logica 58 (1997), S. 273-303 
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    ISSN: 1572-8730
    Keywords: infinitary predicate KD4 ; common knowledge ; Nash equilibrium ; undecidability on playability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Philosophy
    Notes: Abstract This paper provides a Genzten style formulation of the game logic framework GLm (0 ≤ m ≤ ω), and proves the cut-elimination theorem for GLm. As its application, we prove the term existence theorem for GLω used in Part I.
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    URL: http://dx.doi.org/10.1023/A:1004975724824
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    Inverses for Normal Modal Operators (1997)
    Springer
    Studia logica 59 (1997), S. 33-64 
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    ISSN: 1572-8730
    Keywords: modal logic ; Kripke models ; inverses ; conservative extension
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Philosophy
    Notes: Abstract Given a 1-ary sentence operator ○, we describe L - another 1-ary operator - as as a left inverse of ○ in a given logic if in that logic every formula ϕ is provably equivalent to L○ϕ. Similarly R is a right inverse of ○ if ϕ is always provably equivalent to ○Rϕ. We investigate the behaviour of left and right inverses for ○ taken as the □ operator of various normal modal logics, paying particular attention to the conditions under which these logics are conservatively extended by the addition of such inverses, as well as to the question of when, in such extensions, the inverses behave as normal modal operators in their own right.
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    URL: http://dx.doi.org/10.1023/A:1004995316790
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    Combining Possibilities and Negations (1997)
    Springer
    Studia logica 59 (1997), S. 121-141 
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    ISSN: 1572-8730
    Keywords: combining non-classical logics ; intuitionistic logic ; negation ; possibility
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Philosophy
    Notes: Abstract Combining non-classical (or ‘sub-classical’) logics is not easy, but it is very interesting. In this paper, we combine nonclassical logics of negation and possibility (in the presence of conjunction and disjunction), and then we combine the resulting systems with intuitionistic logic. We will find that Kracht's results on the undecidability of classical modal logics generalise to a non-classical setting. We will also see conditions under which intuitionistic logic can be combined with a non-intuitionistic negation without corrupting the intuitionistic fragment of the logic.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1004951501769
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    Synchronization of Logics (1997)
    Springer
    Studia logica 59 (1997), S. 217-247 
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    ISSN: 1572-8730
    Keywords: combination of logics ; synchronization on formulae ; synchronization on models ; temporal logic ; equational logic
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Philosophy
    Notes: Abstract Motivated by applications in software engineering, we propose two forms of combination of logics: synchronization on formulae and synchronization on models. We start by reviewing satisfaction systems, consequence systems, one-step derivation systems and theory spaces, as well as their functorial relationships. We define the synchronization on formulae of two consequence systems and provide a categorial characterization of the construction. For illustration we consider the synchronization of linear temporal logic and equational logic. We define the synchronization on models of two satisfaction systems and provide a categorial characterization of the construction. We illustrate the technique in two cases: linear temporal logic versus equational logic; and linear temporal logic versus branching temporal logic. Finally, we lift the synchronization on formulae to the category of logics over consequences systems.
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    URL: http://dx.doi.org/10.1023/A:1004904401346
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    Cut-Free Tableau Calculi for some Intuitionistic Modal Logics (1997)
    Springer
    Studia logica 59 (1997), S. 303-330 
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    ISSN: 1572-8730
    Keywords: intuitionistic modal logics ; refutation systems ; Kripke models ; duplications
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Philosophy
    Notes: Abstract In this paper we provide cut-free tableau calculi for the intuitionistic modal logics IK, ID, IT, i.e. the intuitionistic analogues of the classical modal systems K, D and T. Further, we analyse the necessity of duplicating formulas to which rules are applied. In order to develop these calculi we extend to the modal case some ideas presented by Miglioli, Moscato and Ornaghi for intuitionistic logic. Specifically, we enlarge the language with the new signs Fc and CR near to the usual signs T and F. In this work we establish the soundness and completeness theorems for these calculi with respect to the Kripke semantics proposed by Fischer Servi.
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    URL: http://dx.doi.org/10.1023/A:1005072627389
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    Note by the Guest Editors (1998)
    Springer
    Studia logica 60 (1998), S. 1-1 
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    ISSN: 1572-8730
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Philosophy
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1005065031956
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    Cut-Elimination and a Permutation-Free Sequent Calculus for Intuitionistic Logic (1998)
    Springer
    Studia logica 60 (1998), S. 107-118 
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    ISSN: 1572-8730
    Keywords: Cut-elimination ; normalisation ; natural deduction ; intuitionistic logic ; recursive path ordering ; termination
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Philosophy
    Notes: Abstract We describe a sequent calculus, based on work of Herbelin, of which the cut-free derivations are in 1-1 correspondence with the normal natural deduction proofs of intuitionistic logic. We present a simple proof of Herbelin's strong cut-elimination theorem for the calculus, using the recursive path ordering theorem of Dershowitz.
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    URL: http://dx.doi.org/10.1023/A:1005099619660
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    On the Logic of Acceptance and Rejection (1998)
    Springer
    Studia logica 60 (1998), S. 233-251 
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    ISSN: 1572-8730
    Keywords: autoepistemic logic
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Philosophy
    Notes: Abstract The logic of acceptance and rejection (AEL2) is a nonmonotonic formalism to represent states of knowledge of an introspective agent making decisions about available information. Though having much in common, AEL2 differs from Moore's autoepistemic logic (AEL) by the fact that the agent not only can accept or reject a given fact, but he/she also has the possibility not to make any decision in case he/she does not have enough knowledge.
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    URL: http://dx.doi.org/10.1023/A:1005009115432
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    Many-Valued Logics and Suszko's Thesis Revisited (1998)
    Springer
    Studia logica 60 (1998), S. 299-309 
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    ISSN: 1572-8730
    Keywords: Suszko's Thesis ; many-valued logics ; q-logics ; bivaluations ; universal logic
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Philosophy
    Notes: Abstract Suszko's Thesis maintains that many-valued logics do not exist at all. In order to support it, R. Suszko offered a method for providing any structural abstract logic with a complete set of bivaluations. G. Malinowski challenged Suszko's Thesis by constructing a new class of logics (called q-logics by him) for which Suszko's method fails. He argued that the key for logical two-valuedness was the "bivalent" partition of the Lindenbaum bundle associated with all structural abstract logics, while his q-logics were generated by "trivalent" matrices. This paper will show that contrary to these intuitions, logical two-valuedness has more to do with the geometrical properties of the deduction relation of a logical structure than with the algebraic properties embedded on it.
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    URL: http://dx.doi.org/10.1023/A:1005020217249
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    Grafting Modalities onto Substructural Implication Systems (1997)
    Springer
    Studia logica 59 (1997), S. 65-102 
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    ISSN: 1572-8730
    Keywords: Kripke semantics ; labelled deductive systems ; KE system
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Philosophy
    Notes: Abstract We investigate the semantics of the logical systems obtained by introducing the modalities □ and ⋄ into the family of substructural implication logics (including relevant, linear and intuitionistic implication). Then, in the spirit of the LDS (Labelled Deductive Systems) methodology, we "import" this semantics into the classical proof system KE. This leads to the formulation of a uniform labelled refutation system for the new logics which is a natural extension of a system for substructural implication developed by the first two authors in a previous paper.
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    URL: http://dx.doi.org/10.1023/A:1004947400860
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    Kripke Frame with Graded Accessibility and Fuzzy Possible World Semantics (1997)
    Springer
    Studia logica 59 (1997), S. 249-269 
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    ISSN: 1572-8730
    Keywords: Kripke semantics ; possible world semantics ; fuzzy
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Philosophy
    Notes: Abstract A possible world structure consist of a set W of possible worlds and an accessibility relation R. We take a partial function r(·,·) to the unit interval [0, 1] instead of R and obtain a Kripke frame with graded accessibility r Intuitively, r(x, y) can be regarded as the reliability factor of y from x We deal with multimodal logics corresponding to Kripke frames with graded accessibility in a fairly general setting. This setting provides us with a framework for fuzzy possible world semantics. The basic propositional multimodal logic gK (grated K) is defined syntactically. We prove that gK is sound and complete with respect to this semantics. We discuss some extensions of gK including logics of similarity relations and of fuzzy orderings. We present a modified filtration method and prove that gK and its extensions introduced here are decidable.
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    URL: http://dx.doi.org/10.1023/A:1004956418185
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    Rules of Existential Quantification into "Intensional Contexts" (1997)
    Springer
    Studia logica 59 (1997), S. 331-343 
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    ISSN: 1572-8730
    Keywords: propositional/notional attitudes ; intensions ; quantification into ; transparent intensional logic ; ramified hierarchy of types
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Philosophy
    Notes: Abstract Propositional and notional attitudes are construed as relations (-in-intension) between individuals and constructions (rather than propositrions etc,). The apparatus of transparent intensional logic (Tichy) is applied to derive two rules that make it possible to ‘export’ existential quantifiers without conceiving attitudes as relations to expressions (‘sententialism’).
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    URL: http://dx.doi.org/10.1023/A:1005032311459
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