Difference between revisions of "On the difference between traditional and deductive fuzzy logic"

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(Post-publication comments: comment on the name deductive fuzzy logics)
(Author's comments: truth degrees as upper intervals)
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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 [[Petr Cintula|Cintula]]'s weakly implicative fuzzy logics and [[Hiroakira Ono|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 [[Fuzzy logics as the logics of chains#Post-publication comments|comments]] there). -- [[User:LBehounek|LBehounek]] 20:30, 2 September 2008 (CEST)
 
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 [[Petr Cintula|Cintula]]'s weakly implicative fuzzy logics and [[Hiroakira Ono|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 [[Fuzzy logics as the logics of chains#Post-publication comments|comments]] there). -- [[User:LBehounek|LBehounek]] 20:30, 2 September 2008 (CEST)
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====Truth degrees as upper intervals====
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In his talk at [http://www.mat.unisi.it/~latd2008 Logic, Algebra and Truth Degrees] in Siena 2008, [[Josep Maria Font]] proposed the ''upper intervals'' <math>[\alpha,\to)=\{\beta\in L\mid\beta\ge\alpha\}</math> to be called '''truth degrees,''' for all truth '''values''' <math>\alpha\in L</math>. This proposal is quite consonant with my description of the "principle of persistence" in the present paper, and I regret that I did not get the idea of presenting the principle of persistence in this way, as it might have been more comprehensible for traditional fuzzy mathematicians than my expression "guaranteed thresholds" found in the paper. The rationale for Font's proposal is that so defined truth degrees, rather than truth values, are preserved by fully true implications (which was also one of the messages of my paper). -- [[User:LBehounek|LBehounek]] 16:09, 25 September 2008 (CEST)
  
  
 
[[Category:FCT publications]]
 
[[Category:FCT publications]]

Revision as of 14:09, 25 September 2008

Authors:
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
Download from the publisher
Preprint





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)

Truth degrees as upper intervals

In his talk at Logic, Algebra and Truth Degrees in Siena 2008, Josep Maria Font proposed the upper intervals Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle [\alpha,\to)=\{\beta\in L\mid\beta\ge\alpha\}} to be called truth degrees, for all truth values Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle \alpha\in L} . This proposal is quite consonant with my description of the "principle of persistence" in the present paper, and I regret that I did not get the idea of presenting the principle of persistence in this way, as it might have been more comprehensible for traditional fuzzy mathematicians than my expression "guaranteed thresholds" found in the paper. The rationale for Font's proposal is that so defined truth degrees, rather than truth values, are preserved by fully true implications (which was also one of the messages of my paper). -- LBehounek 16:09, 25 September 2008 (CEST)