Paper Info
Title
First-order t-norm based fuzzy logics with truth-constants: Distinguished semantics and completeness properties
Abstract
This 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 r¯→φ, where φ has no additional truth-constants.
Year
DOI
Venue
2009
10.1016/j.apal.2009.05.014
Annals of Pure and Applied Logic
Keywords
Field
DocType
03B50,03B52,06B99
T-norm,Discrete mathematics,T-norm fuzzy logics,Łukasiewicz logic,Algebra,Unit interval,Classical logic,Monoidal t-norm logic,Completeness (order theory),Higher-order logic,Mathematics
Journal
Volume
Issue
ISSN
161
2
0168-0072
Citations 
PageRank 
References 
27
1.00
24
Authors
3
Name
Order
Citations
PageRank
Francesc Esteva11885200.14
Lluís Godo288856.28
Carles Noguera346233.93