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  • Articles  (12,252)
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  • American Association for the Advancement of Science (AAAS)  (6,559)
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  • 1990-1994  (3,590)
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  • Articles  (12,252)
  • Other Sources
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  • 2015-2019  (8,662)
  • 2005-2009
  • 1990-1994  (3,590)
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  • 1
    Electronic Resource
    Electronic Resource
    Some independence results in interpretability logic (1991)
    Springer
    Studia logica 50 (1991), S. 29-38 
    Details
    ISSN: 1572-8730
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Philosophy
    Notes: Abstract A Kripke-style semantics developed by de Jongh and Veltman is used to investigate relations between several extensions of interpretability logic, IL.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00370385
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  • 2
    Electronic Resource
    Electronic Resource
    Rosser orderings and free variables (1991)
    Springer
    Studia logica 50 (1991), S. 71-80 
    Details
    ISSN: 1572-8730
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Philosophy
    Notes: Abstract It is shown that for arithmetical interpretations that may include free variables it is not the Guaspari-Solovay system R that is arithmetically complete, but their system R −. This result is then applied to obtain the nonvalidity of some rules under arithmetical interpretations including free variables, and to show that some principles concerning Rosser orderings with free variables cannot be decided, even if one restricts oneself to “usual” proof predicates.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00370388
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  • 3
    Electronic Resource
    Electronic Resource
    Some unifying fixed point principles (1991)
    Springer
    Studia logica 50 (1991), S. 129-141 
    Details
    ISSN: 1572-8730
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Philosophy
    Notes: Abstract This article is written for both the general mathematican and the specialist in mathematical logic. No prior knowledge of metamathematics, recursion theory or combinatory logic is presupposed, although this paper deals with quite general abstractions of standard results in those three areas. Our purpose is to show how some apparently diverse results in these areas can be derived from a common construction. In Section 1 we consider five classical fixed point arguments (or rather, generalizations of them) which we present as problems that the reader might enjoy trying to solve. Solutions are given at the end of the section. In Section 2 we show how all these solutions can be obtained as special cases of a single fixed point theorem. In Section 3 we consider another generalization of the five fixed point results of Section 1 and show that this is of the same strength as that of Section 2. In Section 4 we show some curious strengthenings of results of Section 3 which we believe to be of some interest on their own accounts.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00370391
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  • 4
    Electronic Resource
    Electronic Resource
    Three-membered domains for aristotle's syllogistic (1991)
    Springer
    Studia logica 50 (1991), S. 181-187 
    Details
    ISSN: 1572-8730
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Philosophy
    Notes: Abstract The paper shows that for any invalid polysyllogism there is a procedure for constructing a model with a domain with exactly three members and an interpretation that assigns non-empty, non-universal subsets of the domain to terms such that the model invalidates the polysyllogism.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00370181
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  • 5
    Electronic Resource
    Electronic Resource
    Logical feedback (1991)
    Springer
    Studia logica 50 (1991), S. 225-239 
    Details
    ISSN: 1572-8730
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Philosophy
    Notes: Abstract Just as non-well-founded sets extend the usual sets of ZF, so do root reflexive propositional formulas extends the usual class of Boolean expressions. Though infinitary, these formulas are generated by finite patterns. They possess transition functions instead of truth values and have applications in electric circuit theory.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00370184
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  • 6
    Electronic Resource
    Electronic Resource
    On structural completeness of implicational logics (1991)
    Springer
    Studia logica 50 (1991), S. 275-297 
    Details
    ISSN: 1572-8730
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Philosophy
    Notes: Abstract We consider the notion of structural completeness with respect to arbitrary (finitary and/or infinitary) inferential rules. Our main task is to characterize structurally complete intermediate logics. We prove that the structurally complete extension of any pure implicational in termediate logic C can be given as an extension of C with a certain family of schematically denned infinitary rules; the same rules are used for each C. The cardinality of the family is continuum and, in the case of (the pure implicational fragment of) intuitionistic logic, the family cannot be reduced to a countable one. It means that the structurally complete extension of the intuitionistic logic is not countably axiomatizable by schematic rules.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00370188
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  • 7
    Electronic Resource
    Electronic Resource
    Books received (1991)
    Springer
    Studia logica 50 (1991), S. 351-357 
    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/BF00370193
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  • 8
    Electronic Resource
    Electronic Resource
    Introduction (1991)
    Springer
    Studia logica 50 (1991), S. 365-374 
    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/BF00370677
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  • 9
    Electronic Resource
    Electronic Resource
    A deduction theorem schema for deductive systems of propositional logics (1991)
    Springer
    Studia logica 50 (1991), S. 385-390 
    Details
    ISSN: 1572-8730
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Philosophy
    Notes: Abstract We propose a new schema for the deduction theorem and prove that the deductive system S of a prepositional logic L fulfills the proposed schema if and only if there exists a finite set A(p, q) of propositional formulae involving only prepositional letters p and q such that A(p, p) ⊑ L and p, A(p, q) ⊢s q.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00370679
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  • 10
    Electronic Resource
    Electronic Resource
    Construction of monadic three-valued Łukasiewicz algebras (1991)
    Springer
    Studia logica 50 (1991), S. 473-483 
    Details
    ISSN: 1572-8730
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Philosophy
    Notes: Abstract The notion of monadic three-valued Łukasiewicz algebras was introduced by L. Monteiro ([12], [14]) as a generalization of monadic Boolean algebras. A. Monteiro ([9], [10]) and later L. Monteiro and L. Gonzalez Coppola [17] obtained a method for the construction of a three-valued Łukasiewicz algebra from a monadic Boolea algebra. In this note we give the construction of a monadic three-valued Łukasiewicz algebra from a Boolean algebra B where we have defined two quantification operations ∃ and ∃* such that ∃∀*x=∀*∃x (where ∀*x=-∃*-x). In this case we shall say that ∃ and ∃* commutes. If B is finite and ∃ is an existential quantifier over B, we shall show how to obtain all the existential quantifiers ∃* which commute with ∃. Taking into account R. Mayet [3] we also construct a monadic three-valued Łukasiewicz algebra from a monadic Boolean algebra B and a monadic ideal I of B. The most essential results of the present paper will be submitted to the XXXIX Annual Meeting of the Unión Matemática Argentina (October 1989, Rosario, Argentina).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00370683
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