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  • 1
    Digitale Medien
    Digitale Medien
    Ayda Ignez Arruda (1936–1983) (1984)
    Springer
    Studia logica 43 (1984), S. 1-2 
    Details
    ISSN: 1572-8730
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik , Philosophie
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00935735
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  • 2
    Digitale Medien
    Digitale Medien
    Paraconsistent logic and model theory (1984)
    Springer
    Studia logica 43 (1984), S. 17-32 
    Details
    ISSN: 1572-8730
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik , Philosophie
    Notizen: Abstract The object of this paper is to show how one is able to construct a paraconsistent theory of models that reflects much of the classical one. In other words the aim is to demonstrate that there is a very smooth and natural transition from the model theory of classical logic to that of certain categories of paraconsistent logic. To this end we take an extension of da Costa'sC 1 = (obtained by adding the axiom ⌝⌝A ↔A) and prove for it results which correspond to many major classical model theories, taken from Shoenfield [5]. In particular we prove counterparts of the theorems of Łoś-Tarski and Chang-Łoś-Suszko, Craig-Robinson and the Beth definability theorem.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00935737
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  • 3
    Digitale Medien
    Digitale Medien
    On the relevant systemsP andP * and some related systems (1984)
    Springer
    Studia logica 43 (1984), S. 33-49 
    Details
    ISSN: 1572-8730
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik , Philosophie
    Notizen: Abstract In this paper we study the systemsP andP * (see Arruda and da Costa,O paradoxo de Curry-Moh Shaw-Kwei, Boletim da Sociedade Matemātica de São Paulo 18 (1966)) and some related systems. In the last section, we prove that certain set theories havingP andP * as their underlying logics are non-trivial.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00935738
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  • 4
    Digitale Medien
    Digitale Medien
    Zeno's paradoxes and temporal becoming in dialectical atomism (1984)
    Springer
    Studia logica 43 (1984), S. 169-180 
    Details
    ISSN: 1572-8730
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik , Philosophie
    Notizen: Abstract The homogeneity of time (i.e. the fact that there are no privileged moments) underlies a fundamental symmetry relating to the energy conservation law. On the other hand the obvious asymmetry between past and future, expressed by the metaphor of the “arrow of time” or “flow of time” accounts for the irreversibility of what happens. One takes this for granted but the conceptual tension it creates against the background of time's presumed homogeneity calls for an explanation of temporal becoming. Here, it is approached with the help of a claim to the effect that the instant (moment) itself has a structure isomorphic to that of time as a whole. Then the asymmetry of past and future in regard to temporal becoming is associated with the internal structure of the very moment, and not with external relations between different moments of time. In this paper ideas of ancient atomism and contemporary dialectics are brought together. It is for the sake of a contrast to what is known as logical atomism that I choose to call this view dialectical atomism. The latter admits dialectical contradictions and, so far as the logical status of contradictions is concerned, bears reference to paraconsistent logics. In the paper there is an outline of a method of converting any consistent axiomatic formal system into a paraconsistent theory.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00935748
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  • 5
    Digitale Medien
    Digitale Medien
    The preservation of coherence (1984)
    Springer
    Studia logica 43 (1984), S. 89-106 
    Details
    ISSN: 1572-8730
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik , Philosophie
    Notizen: Abstract It is argued that the preservation of truth by an inference relation is of little interest when premiss sets are contradictory. The notion of a level of coherence is introduced and the utility of modal logics in the semantic representation of sets of higher coherence levels is noted. It is shown that this representative role cannot be transferred to first order logic via frame theory since the modal formulae expressing coherence level restrictions are not first order definable. Finally, an inference relation, calledyielding, is introduced which is intermediate between the coherence preservingforcing relation introduced elsewhere by the authors and the coherence destroying, inference relation of classical logic.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00935743
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  • 6
    Digitale Medien
    Digitale Medien
    Aristotle's thesis in consistent and inconsistent logics (1984)
    Springer
    Studia logica 43 (1984), S. 107-116 
    Details
    ISSN: 1572-8730
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik , Philosophie
    Notizen: Abstract A typical theorem of conaexive logics is Aristotle's Thesis(A), ∼(A→∼A).A cannot be added to classical logic without producing a trivial (Post-inconsistent) logic, so connexive logics typically give up one or more of the classical properties of conjunction, e.g.(A & B)→A, and are thereby able to achieve not only nontriviality, but also (negation) consistency. To date, semantical modellings forA have been unintuitive. One task of this paper is to give a more intuitive modelling forA in consistent logics. In addition, while inconsistent but nontrivial theories, and inconsistent nontrivial logics employing prepositional constants (for which the rule of uniform substitution US fails), have both been studied extensively within the paraconsistent programme, inconsistent nontrivial logics (closed under US) do not seem to have been. This paper gives sufficient conditions for a logic containingA to be inconsistent, and then shows that there is a class of inconsistent nontrivial logics all containingA. A second semantical modelling forA in such logics is given. Finally, some informal remarks about the kind of modellingA seems to require are made.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00935744
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  • 7
    Digitale Medien
    Digitale Medien
    Some independence results in interpretability logic (1991)
    Springer
    Studia logica 50 (1991), S. 29-38 
    Details
    ISSN: 1572-8730
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik , Philosophie
    Notizen: Abstract A Kripke-style semantics developed by de Jongh and Veltman is used to investigate relations between several extensions of interpretability logic, IL.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00370385
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  • 8
    Digitale Medien
    Digitale Medien
    Rosser orderings and free variables (1991)
    Springer
    Studia logica 50 (1991), S. 71-80 
    Details
    ISSN: 1572-8730
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik , Philosophie
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00370388
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  • 9
    Digitale Medien
    Digitale Medien
    Some unifying fixed point principles (1991)
    Springer
    Studia logica 50 (1991), S. 129-141 
    Details
    ISSN: 1572-8730
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik , Philosophie
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00370391
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  • 10
    Digitale Medien
    Digitale Medien
    Three-membered domains for aristotle's syllogistic (1991)
    Springer
    Studia logica 50 (1991), S. 181-187 
    Details
    ISSN: 1572-8730
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik , Philosophie
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00370181
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