Search results for "Algebraic semantics"

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Duality, projectivity, and unification in Łukasiewicz logic and MV-algebras

2013

AbstractWe prove that the unification type of Łukasiewicz (infinite-valued propositional) logic and of its equivalent algebraic semantics, the variety of MV-algebras, is nullary. The proof rests upon Ghilardiʼs algebraic characterisation of unification types in terms of projective objects, recent progress by Cabrer and Mundici in the investigation of projective MV-algebras, the categorical duality between finitely presented MV-algebras and rational polyhedra, and, finally, a homotopy-theoretic argument that exploits lifts of continuous maps to the universal covering space of the circle. We discuss the background to such diverse tools. In particular, we offer a detailed proof of the duality …

Fundamental groupPure mathematicsUnificationŁukasiewicz logic; Unification; Projective MV-algebras; Rational polyhedra; Fundamental group; Covering spaceLogicCovering spaceDuality (mathematics)Projective MV-algebrasMV-algebraCovering spaceŁukasiewicz logicRational polyhedraAlgebraAlgebraic semanticsUnificationVariety (universal algebra)Algebraic numberŁukasiewicz logicMathematicsAnnals of Pure and Applied Logic
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