A general view of the algebraic semantics of Lukasiewicz logic with product
نویسنده
چکیده
This paper aims to give a clear and comprehensive view of the relations between the various classes of MV-algebras with product operations. The algebraic hyerarchy, from groups to algebras, can be transported by Γ-functors in order to provide the algebraic semantics for conservative extensions of Łukasiewicz logic. The MV-algebraic tensor product allows us to complete the picture with categorical adjunctions. On our way, we define the tensor PMV-algebra of a semisimple MV-algebra, inspired by the construction of the tensor algebra of a vector space. We further prove amalgamation properties and we translate all results in the framework of lattice-ordered groups.
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