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Title

Expanding the propositional logic of a t-norm with truth-constants: completeness results for rational semantics

AuthorsEsteva, Francesc ; Godo, Lluis ; Noguera, Carles
KeywordsLeft-continuous t-norms
Evaluated formulae
Mathematical fuzzy logic
Truth-constants
Realand rational completeness
T-norm based logics
Issue Date2010
PublisherSpringer
CitationSoft Computing 14: 273- 284 (2010)
AbstractIn this paper we consider the expansions of logics of a left-continuous t-norm with truth-constants from a subalgebra of the rational unit interval. From known results on standard semantics, we study completeness for these propositional logics with respect to chains deined over the rational unit interval with a special attention to the completeness with respect to the canonical chain, i.e. the algebra over $[0, 1] \cap Q$ where each truth-constant is interpreted in its corresponding rational truth-value. Finally, we study rational completeness results when we restrict ourselves to deductions between the so-called evaluated formulae.
URIhttp://hdl.handle.net/10261/160412
DOIhttp://dx.doi.org/10.1007/s00500-009-0402-8
Identifiersdoi: 10.1007/s00500-009-0402-8
issn: 1432-7643
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