A Note on Axiomatizations of Pavelka-style Complete Fuzzy Logics

0436177 - ÚI 2016 RIV NL eng J - Journal Article
Cintula, Petr
A Note on Axiomatizations of Pavelka-style Complete Fuzzy Logics.
Fuzzy Sets and Systems. Roč. 292, 1 June (2016), s. 160-174. ISSN 0165-0114. E-ISSN 1872-6801
R&D Projects: GA ČR GAP202/10/1826
Institutional support: RVO:67985807
Keywords : mathematical fuzzy logic * Pavelka-style completeness * MTL logic * Lukasiewicz logics * Product Logic * truth constants * Monteiro–Baaz delta
OECD category: Pure mathematics
Impact factor: 2.718, year: 2016

Pavelka-style completeness, a property relating degrees of provability and truth, was previously studied mainly in the context of logics with continuous connectives. It is known that in some other logics one can use infinitary deduction rule(s) to retain this form of completeness. The present paper offers a systematic study of this idea for fuzzy logics which expand MTL and are given by a fixed standard algebra. We explore the structure of the class of all ’reasonable’ expansions of any such logic by rational truth constants and, for several prominent cases, provide axiomatizations of particular expansions enjoying the Pavelka-style completeness.
Permanent Link: http://hdl.handle.net/11104/0239961