Partial algebras for Łukasiewicz logics and its extensions

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Authors:
Thomas Vetterlein
Title: Partial algebras for Łukasiewicz logics and its extensions
Journal: Archive for Mathematical Logic
Volume 44
Number
Pages: 913 - 933
Year: 2005





Abstract

We consider several logics differing from Lukasiewicz logics in that they contain further connectives: the logic PL, PL', PL'Δ, and LΠ. For their algebraic counterparts, we characterise the corresponding type of partial algebras; and we moreover consider the representing f-rings, constructed in a transparent way from the partial algebras - just like po-groups from effect algebras. All in all, we get three-fold correspondences: the total algebras - the partial algebras - the representing rings.