Deduction in many-valued logics: a survey.
Reiner Hähnle, Gonzalo Escalada-Imaz (1997)
Mathware and Soft Computing
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Reiner Hähnle, Gonzalo Escalada-Imaz (1997)
Mathware and Soft Computing
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Frank Klawonn, Rudolf Kruse (1994)
Mathware and Soft Computing
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Prolog is a programming language based on a restricted subset of classical first order predicate logic. In order to overcome some problems of classical logic to handle imperfect human knowledge, we provide a formal framework for a Lukasiewicz logic based Prolog system. The use of Lukasiewicz logic with its connection to Ulam games enables us to deal with partial inconsistencies by interpreting the truth values as relative distance to contradiction. We also present the software tool LULOG...
Dale Jacquette (2005)
Philosophia Scientiae
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Michel Bourdeau (2003)
Philosophia Scientiae
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Contrairement à ce qui a parfois été dit, la logique classique et la logique intuitionniste ne s’opposent pas comme une logique de l’existence à une logique de la connaissance. Les considérations épistémologiques trouvent naturellement leur place dans le cadre de la logique classique, sans qu’il soit nécessaire de faire intervenir aucun principe intuitionniste ; il suffit pour cela de reconnaître que la logique ne peut se passer de la notion d’assertion, ou si l’on préfère de jugement....
Javier Legris, Jorge A. Molina (2001)
Philosophia Scientiae
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In this paper we analyze the consideration of intuitionistic logic as an extension of classical logic. This — at first sight surprising — point of view has been sustained explicitly by Jan Łukasiewicz on the basis of a mapping of classical propositional logic into intuitionistic propositional logic by Kurt Gödel in 1933. Simultaneously with Gödel, Gerhard Gentzen had proposed another mapping of Peano´s arithmetic into Heyting´s arithmetic. We shall discuss these mappings in connection...
Arkadiusz Wójcik (2020)
Bulletin of the Section of Logic
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The dynamic epistemic logic for actual knowledge models the phenomenon of actual knowledge change when new information is received. In contrast to the systems of dynamic epistemic logic which have been discussed in the past literature, our system is not burdened with the problem of logical omniscience, that is, an idealized assumption that the agent explicitly knows all classical tautologies and all logical consequences of his or her knowledge. We provide a sound and complete axiomatization...
María Manzano, Manuel Crescencio Moreno (2018)
Bulletin of the Section of Logic
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This article is a continuation of our promenade along the winding roads of identity, equality, nameability and completeness. We continue looking for a place where all these concepts converge. We assume that identity is a binary relation between objects while equality is a symbolic relation between terms. Identity plays a central role in logic and we have looked at it from two different points of view. In one case, identity is a notion which has to be defined and, in the other case, identity...
Krister Segerberg (1982)
Banach Center Publications
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Guido Gherardi, Eugenio Orlandelli (2021)
Bulletin of the Section of Logic
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This paper introduces the logics of super-strict implications, where a super-strict implication is a strengthening of C.I. Lewis' strict implication that avoids not only the paradoxes of material implication but also those of strict implication. The semantics of super-strict implications is obtained by strengthening the (normal) relational semantics for strict implication. We consider all logics of super-strict implications that are based on relational frames for modal logics in the...
Slobodan Vujošević (2012)
Review of the National Center for Digitization
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Josep Font (1993)
Banach Center Publications
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The aim of this paper is to discuss the motivation for a new general algebraic semantics for deductive systems, to introduce it, and to present an outline of its main features. Some tools from the theory of abstract logics are also introduced, and two classifications of deductive systems are analysed: one is based on the behaviour of the Leibniz congruence (the maximum congruence of a logical matrix) and the other on the behaviour of the Frege operator (which associates to every theory...
Chris Brink (1993)
Banach Center Publications
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The purpose of this note is to show that a known and natural four-valued logic co-exists with classical two-valued logic in the familiar context of truth tables. The tool required is the power construction.
Lau, Raymond, Wong, On (2000)
Novi Sad Journal of Mathematics
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