On the difference between traditional and deductive fuzzy logic

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Revision as of 18:30, 2 September 2008 by LBehounek (talk | contribs) (Post-publication comments: comment on the name deductive fuzzy logics)

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Libor Běhounek
Title: On the difference between traditional and deductive fuzzy logic
Journal: Fuzzy Sets and Systems
Volume 159
Number 10
Pages: 1153-1164
Year: 2008
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Post-publication comments

Author's comments

Relation to the program of the Manifesto

The paper delimits the area of logic-based fuzzy mathematics more narrowly than an earlier paper From fuzzy logic to fuzzy mathematics: a methodological manifesto, which (following the optimism of Hájek's 1998 monograph) assumed that formal fuzzy logic can give foundations to all fuzzy mathematics. However, it turned out that traditional fuzzy mathematics actually deals with too many different phenomena and is in fact composed of several completely different parts. The field in which the logic-based approach is most fruitful is marked by a clear interpretation of membership degrees as degrees of truth (preserved under inference), while other areas of fuzzy mathematics work with a mixture of other notions of `degrees' (often not clarified enough). Naturally, logic-based methods apply less straightforwardly to such fields, even though formal fuzzy logic can sometimes help there as well. The paper therefore presents rather a more precise delimitation of the area of research than a retreat from the foundational program. -- LBehounek 16:35, 2 September 2008 (CEST)

The name of the class of logics

The name deductive fuzzy logic is in the paper applied both to a discipline and to a formally delimited class of logics (viz the intersection of the classes of Cintula's weakly implicative fuzzy logics and Ono's substructural logics as the logics of residuated lattices). As argued in a comment to the paper Fuzzy logics as the logics of chains, a better name for the class could perhaps be semilinear substructural logics (see the comments there). -- LBehounek 20:30, 2 September 2008 (CEST)