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 Volume 14 Pagination 273-284 Publisher Springer Abstract 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.