Institute of Information Theory and Automation

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Bibliography

Monography Chapter

The Quest for the Basic Fuzzy Logic

Cintula Petr, Horčík Rostislav, Noguera Carles

: Petr Hájek on Mathematical Fuzzy Logic, p. 245-290 , Eds: Montagna F.

: GAP202/10/1826, GA ČR, GA13-14654S, GA ČR, 247584, EC, TIN2010-20967-C04-01, MICINN project TASSAT

: mathematical fuzzy logic, basic fuzzy logic, T-norm, core fuzzy logics, core semilinear logics, non-associative substructural logics, standard completeness

: 10.1007/978-3-319-06233-4_12

(eng): The quest for basic fuzzy logic was initiated by Petr Hájek when he proposed his basic fuzzy logic BL, complete with respect to the semantics given by all continuous t-norms. Later weaker systems, such as MTL, UL or psMT^r, complete with respect to broader (but still meaningful for fuzzy logics) semantics, have been introduced and disputed the throne of the basic fuzzy logic. We contribute to the quest with our own proposal of a basic fuzzy logic. Indeed, we put forth a very weak logic calleda SL^\ell, introduced and studied in earlier works of the authors, and propose it as a base of a new framework which allows to work in a uniform way with both propositional and first-order fuzzy logics.

: BA

2019-01-07 08:39