Petr Hájek on Mathematical Fuzzy Logic

0432930 - ÚI 2015 RIV CH eng M - Monography Chapter
Cintula, Petr - Horčík, Rostislav - Noguera, Carles
The Quest for the Basic Fuzzy Logic.
Petr Hájek on Mathematical Fuzzy Logic. Cham: Springer, 2015 - (Montagna, F.), s. 245-290. Outstanding Contributions to Logic, 6. ISBN 978-3-319-06232-7
R&D Projects: GA ČR GAP202/10/1826; GA ČR GA13-14654S
EU Projects: European Commission(XE) 247584 - MATOMUVI
Grant - others:MICINN project TASSAT(XE) TIN2010-20967-C04-01
Institutional support: RVO:67985807 ; RVO:67985556
Keywords : mathematical fuzzy logic * basic fuzzy logic * T-norm * core fuzzy logics * core semilinear logics * non-associative substructural logics * standard completeness
Subject RIV: BA - General Mathematics

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.
Permanent Link: http://hdl.handle.net/11104/0237239