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arXiv · 1411.4987

A general view of the algebraic semantics of \L ukasiewicz logic with product

Serafina Lapenta·Ioana Leustean
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Abstract

This paper aims at connecting the various classes that provide an algebraic semantics for three different conservative expansions of Lukasiewicz logic, using algebraic and category-theoretical techniques. We connect such classes of algebras by adjunctions, using the tensor product of MV-algebras and defining the tensor PMV-algebra of a semisimple MV-algebra, inspired by the construction of the tensor algebra of a vector space. We further apply the main results to prove amalgamation properties and, via categorical equivalence, we transfer all results to the framework of lattice- ordered groups.

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BibTeXRIS

Serafina Lapenta, Ioana Leustean. 2014-11-18. A general view of the algebraic semantics of \L ukasiewicz logic with product. https://arxiv.org/abs/1411.4987

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