Pavelka-style completeness in expansions of Łukasiewicz logic

Details Pavelka-style completeness in expansions of Łukasiewicz logic Pavelka-style completeness in expansions of Łukasiewicz logic

2008-06-30

arxiv.org/abs/0806.4949v1

Archive for Mathematical Logic, 05.03.2008, vol. 47, no. 1, pp. 15-23

Mathematics

Logic

Scientific paper

An algebraic setting for the validity of Pavelka style completeness for some natural expansions of \L ukasiewicz logic by new connectives and rational constants is given. This algebraic approach is based on the fact that the standard MV-algebra on the real segment $[0, 1]$ is an injective MV-algebra. In particular the logics associated with MV-algebras with product and with divisible MV-algebras are considered.

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