Expanding the propositional logic of a t-norm with truth-constants: completeness results for rational semantics
|Title:||Expanding the propositional logic of a t-norm with truth-constants: completeness results for rational semantics|
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In this paper we consider the expansions of logics associated to a (left-continuous) t-norm with countable algebras of truth-constants. 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 rational unit interval 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.