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First-order t-norm based fuzzy logics with truth-constants: Distinguished semantics and completeness properties

AuthorsEsteva, Francesc ; Godo, Lluis ; Noguera, Carles
T-norm based fuzzy logics
Residuated lattices
Mathematical fuzzy logic
First-order predicate non-classical logics
Algebraic logic
Issue Date2009
CitationAnnals of Pure and Applied Logic 161: 185- 202 (2009)
AbstractThis paper aims at being a systematic investigation of different completeness properties of first-order predicate logics with truth-constants based on a large class of left-continuous t-norms (mainly continuous and weak nilpotent minimum t-norms). We consider standard semantics over the real unit interval but also we explore alternative semantics based on the rational unit interval and on finite chains. We prove that expansions with truth-constants are conservative and we study their real, rational and finite chain completeness properties. Particularly interesting is the case of considering canonical real and rational semantics provided by the algebras where the truth-constants are interpreted as the numbers they actually name. Finally, we study completeness properties restricted to evaluated formulae of the kind over(r, -) → φ, where φ has no additional truth-constants. © 2009 Elsevier B.V. All rights reserved.
Identifiersdoi: 10.1016/j.apal.2009.05.014
issn: 0168-0072
Appears in Collections:(IIIA) Artículos
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