|Title||Expanding the propositional logic of a t-norm with truth-constants: completeness results for rational semantics|
|Publication Type||Journal Article|
|Year of Publication||2010|
|Authors||Esteva F, Godo L, Noguera C|
|Journal||Soft Computing - A Fusion of Foundations, Methodologies and Applications|
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 de?ned 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.
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