Distinguished algebraic semantics for t -norm based fuzzy logics: Methods and algebraic equivalencies
Annals of Pure and Applied Logic 160 (1):53-81 (2009)
Abstract
This paper is a contribution to Mathematical fuzzy logic, in particular to the algebraic study of t-norm based fuzzy logics. In the general framework of propositional core and Δ-core fuzzy logics we consider three properties of completeness with respect to any semantics of linearly ordered algebras. Useful algebraic characterizations of these completeness properties are obtained and their relations are studied. Moreover, we concentrate on five kinds of distinguished semantics for these logics–namely the class of algebras defined over the real unit interval, the rational unit interval, the hyperreals , the strict hyperreals and finite chains, respectively–and we survey the known completeness methods and results for prominent logics. We also obtain new interesting relations between the real, rational and hyperreal semantics, and good characterizations for the completeness with respect to the semantics of finite chains. Finally, all completeness properties and distinguished semantics are also considered for the first-order versions of the logics where a number of new results are provedAuthor's Profile
DOI
10.1016/j.apal.2009.01.012
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Citations of this work
Structural Completeness in Fuzzy Logics.Petr Cintula & George Metcalfe - 2009 - Notre Dame Journal of Formal Logic 50 (2):153-182.
Löwenheim–Skolem theorems for non-classical first-order algebraizable logics: Table 1.Pilar Dellunde, Àngel García-Cerdaña & Carles Noguera - 2016 - Logic Journal of the IGPL 24 (3):321-345.
Implicational logics III: completeness properties.Petr Cintula & Carles Noguera - 2018 - Archive for Mathematical Logic 57 (3-4):391-420.
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Logics without the contraction rule.Hiroakira Ono & Yuichi Komori - 1985 - Journal of Symbolic Logic 50 (1):169-201.
Substructural Fuzzy Logics.George Metcalfe & Franco Montagna - 2007 - Journal of Symbolic Logic 72 (3):834 - 864.
Weakly Implicative (Fuzzy) Logics I: Basic Properties. [REVIEW]Petr Cintula - 2006 - Archive for Mathematical Logic 45 (6):673-704.