Displaying similar documents to “On completeness results for Predicate Lukasiewicz, Product, Gödel and Nilpotent Minimum Logics Expanded with Truth-constants.”

Hypersequents and fuzzy logic.

Dov Gabbay, George Metcalfe, Nicola Olivetti (2004)

RACSAM

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Fuzzy logics based on t-norms and their residua have been investigated extensively from a semantic perspective but a unifying proof theory for these logics has, until recently, been lacking. In this paper we survey results of the authors and others which show that a suitable proof-theoretic framework for fuzzy logics is provided by hypersequents, a natural generalization of Gentzen-style sequents. In particular we present hypersequent calculi for the logic of left-continuous t-norms...

A Lukasiewicz logic based Prolog.

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...

How to make your logic fuzzy.

Dov M. Gabbay (1996)

Mathware and Soft Computing

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The aim of this paper is to provide a methodology for turning a known crisp logic into a fuzzy system. We require of the methodology that it be meaningful in general terms, using processes which are independent of the notion of fuzziness, and that it yield a considerable number of known fuzzy systems.

A note on paracomplete logic

Newton C. A. da Costa, Diego Marconi (1986)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

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In questa nota gli Autori descrivono nuovi sistemi di logica (detta «paracompleta») connessi con la logica della vaghezza («fuzzy logic») e con le logiche paraconsistenti.

A note on paracomplete logic

Newton C. A. da Costa, Diego Marconi (1986)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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In questa nota gli Autori descrivono nuovi sistemi di logica (detta «paracompleta») connessi con la logica della vaghezza («fuzzy logic») e con le logiche paraconsistenti.

Truth and utility in fuzzy logic.

Alejandro Sobrino (1999)

Mathware and Soft Computing

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The notion of degree of truth used in fuzzy logic can be interpreted in terms of partial truth or in terms of utility. By investigating how these interpretations fit in with Tarski's definition of truth, this paper explores some of their implications and their consequences for the foundations and credibility of fuzzy logic.

Intuitionistic logic considered as an extension of classical logic : some critical remarks

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...