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

摘要

In 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 defined over the rational unit interval with a special attention to the completeness with respect to the canonical chain, i.e. the algebra over 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. Keywords Mathematical fuzzy logic - Left-continuous t-norms - T-norm based logics - Truth-constants - Evaluated formulae - Real and rational completeness This is an extended and revised version of the paper Rational Completeness Results for Prominent Propositional Fuzzy Logics with Truth-Constants. Proc. of ESTYLF’08, Mieres, Spain, pp. 133–139.