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  • 1
    Electronic Resource
    Electronic Resource
    Errata (1986)
    Springer
    Studia logica 45 (1986), S. 2-2 
    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/BF01881543
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  • 2
    Electronic Resource
    Electronic Resource
    Craig's interpolation theorem for the intuitionistic logic and its extensions—A semantical approach (1986)
    Springer
    Studia logica 45 (1986), S. 19-33 
    Details
    ISSN: 1572-8730
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Philosophy
    Notes: Abstract A semantical proof of Craig's interpolation theorem for the intuitionistic predicate logic and some intermediate prepositional logics will be given. Our proof is an extension of Henkin's method developed in [4]. It will clarify the relation between the interpolation theorem and Robinson's consistency theorem for these logics and will enable us to give a uniform way of proving the interpolation theorem for them.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01881546
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  • 3
    Electronic Resource
    Electronic Resource
    Interpolation and amalgamation properties in varieties of equivalential algebras (1986)
    Springer
    Studia logica 45 (1986), S. 35-38 
    Details
    ISSN: 1572-8730
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Philosophy
    Notes: Abstract Important positive as well as negative results on interpolation property in fragments of the intuitionistic propositional logic (INT) were obtained by J. I. Zucker in [6]. He proved that the interpolation theorem holds in purely implicational fragment of INT. He also gave an example of a fragment of INT for which interpolation fails. This fragment is determined by the constant falsum (⊥), well known connectives: implication (→) and conjunction (∧), and by a ternary connective δ defined as follows: δ (p, q, r)= df (p∧q)∨(ℸp∧r). Extending this result of J. I. Zucker, G. R. Renardel de Lavalette proved in [5] that there are continuously many fragments of INT without the interpolation property. This paper is meant to continue the research mentioned above. To be more precise, its aim is to answer questions concerning interpolation and amalgamation properties in varieties of equivalential algebras, particularly in the variety determined by the purely equivalential fragment of INT.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01881547
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  • 4
    Electronic Resource
    Electronic Resource
    A cut-free gentzen-type system for the logic of the weak law of excluded middle (1986)
    Springer
    Studia logica 45 (1986), S. 39-53 
    Details
    ISSN: 1572-8730
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Philosophy
    Notes: Abstract The logic of the weak law of excluded middleKC p is obtained by adding the formula ℸA ∨ ℸ ℸA as an axiom scheme to Heyting's intuitionistic logicH p . A cut-free sequent calculus for this logic is given. As the consequences of the cut-elimination theorem, we get the decidability of the propositional part of this calculus, its separability, equality of the negationless fragments ofKC p andH p , interpolation theorems and so on. From the proof-theoretical point of view, the formulation presented in this paper makes clearer the relations betweenKC p ,H p , and the classical logic. In the end, an interpretation of classical propositional logic in the propositional part ofKC p is given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01881548
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  • 5
    Electronic Resource
    Electronic Resource
    Logics of some kripke frames connected with Medvedev notion of informational types (1986)
    Springer
    Studia logica 45 (1986), S. 101-118 
    Details
    ISSN: 1572-8730
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Philosophy
    Notes: Abstract Intermediate prepositional logics we consider here describe the setI(Ω) of regular informational types introduced by Yu. T. Medvedev [7]. He showed thatI(Ω) is a Heyting algebra. This algebra gives rise to the “logic of infinite problems” from [13] denoted here asLM 1. Some other definitions of negation inI(Ω) lead to logicsLM n (n ⩽ ω). We study inclusions between these and other systems, proveLM n to be non-finitely axiomatizable (n ⩽ ω) and recursively axiomatizable (n 〈 ω). We also show that formulas in one variable do not separateLM ∞ from Heyting's logicH, andLM n (n 〈 ω) from Scott's logic (H+S).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01881552
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  • 6
    Electronic Resource
    Electronic Resource
    Why objects exist but events occur (1986)
    Springer
    Studia logica 45 (1986), S. 371-375 
    Details
    ISSN: 1572-8730
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Philosophy
    Notes: Abstract I distinguish between sentences like (1) Last Thursday we drove from Wellington to Waikanae and (2) Last Thursday my copy of Aspects of the Theory of Syntax remained on my bookshelf. Sentence (2) has the subinterval property. If it is true at an interval t it is true at every subinterval of t. (1) lacks this property. (1) reports an event. (2) reports a state. Events do not have the subinterval property but states do have it, and so do objects. If something is a linguist at an interval t then that person is a linguist at all subintervals of t. I argue that ‘exists’ applies to things which have the subdinterval property, and ‘occurs’ applies to things which lack it.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00370270
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  • 7
    Electronic Resource
    Electronic Resource
    On decidable consequence operators (1986)
    Springer
    Studia logica 45 (1986), S. 415-424 
    Details
    ISSN: 1572-8730
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Philosophy
    Notes: Abstract The main theorem says that a consequence operator is an effective part of the consequence operator for the classical prepositional calculus iff it is a consequence operator for a logic satisfying the compactness theorem, and in which every finitely axiomatizable theory is decidable.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00370274
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  • 8
    Electronic Resource
    Electronic Resource
    A Completeness Proof for a Logic with an Alternative Necessity Operator (1997)
    Springer
    Studia logica 58 (1997), S. 99-112 
    Details
    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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  • 9
    Electronic Resource
    Electronic Resource
    A Logic for Information Systems (1997)
    Springer
    Studia logica 58 (1997), S. 3-16 
    Details
    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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  • 10
    Electronic Resource
    Electronic Resource
    Fuzzy Logic and Arithmetical Hierarchy, II (1997)
    Springer
    Studia logica 58 (1997), S. 129-141 
    Details
    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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