11 found
Order:
  1. Duality, projectivity, and unification in Łukasiewicz logic and MV-algebras.Vincenzo Marra & Luca Spada - 2013 - Annals of Pure and Applied Logic 164 (3):192-210.
    We prove that the unification type of Łukasiewicz 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 (...)
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   7 citations  
  2.  62
    The Dual Adjunction between MV-algebras and Tychonoff Spaces.Vincenzo Marra & Luca Spada - 2012 - Studia Logica 100 (1-2):253-278.
    We offer a proof of the duality theorem for finitely presented MV-algebras and rational polyhedra, a folklore and yet fundamental result. Our approach develops first a general dual adjunction between MV-algebras and subspaces of Tychonoff cubes, endowed with the transformations that are definable in the language of MV-algebras. We then show that this dual adjunction restricts to a duality between semisimple MV-algebras and closed subspaces of Tychonoff cubes. The duality theorem for finitely presented objects is obtained by a further specialisation. (...)
    Direct download (6 more)  
     
    Export citation  
     
    Bookmark   7 citations  
  3.  15
    Computing coproducts of finitely presented Gödel algebras.Ottavio M. D’Antona & Vincenzo Marra - 2006 - Annals of Pure and Applied Logic 142 (1):202-211.
    We obtain an algorithm to compute finite coproducts of finitely generated Gödel algebras, i.e. Heyting algebras satisfying the prelinearity axiom =1. We achieve this result using ordered partitions of finite sets as a key tool to investigate the category opposite to finitely generated Gödel algebras . We give two applications of our main result. We prove that finitely presented Gödel algebras have free products with amalgamation; and we easily obtain a recursive formula for the cardinality of the free Gödel algebra (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   6 citations  
  4.  40
    The Problem of Artificial Precision in Theories of Vagueness: A Note on the Rôle of Maximal Consistency.Vincenzo Marra - 2014 - Erkenntnis 79 (5):1015-1026.
    The problem of artificial precision is a major objection to any theory of vagueness based on real numbers as degrees of truth. Suppose you are willing to admit that, under sufficiently specified circumstances, a predication of “is red” receives a unique, exact number from the real unit interval [0, 1]. You should then be committed to explain what is it that determines that value, settling for instance that my coat is red to degree 0.322 rather than 0.321. In this note (...)
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  5. Polyhedral Completeness of Intermediate Logics: The Nerve Criterion.Sam Adam-day, Nick Bezhanishvili, David Gabelaia & Vincenzo Marra - 2024 - Journal of Symbolic Logic 89 (1):342-382.
    We investigate a recently devised polyhedral semantics for intermediate logics, in which formulas are interpreted in n-dimensional polyhedra. An intermediate logic is polyhedrally complete if it is complete with respect to some class of polyhedra. The first main result of this paper is a necessary and sufficient condition for the polyhedral completeness of a logic. This condition, which we call the Nerve Criterion, is expressed in terms of Alexandrov’s notion of the nerve of a poset. It affords a purely combinatorial (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark  
  6.  20
    De Finetti’s No-Dutch-Book Criterion for Gödel logic.Stefano Aguzzoli, Brunella Gerla & Vincenzo Marra - 2008 - Studia Logica 90 (1):25-41.
    We extend de Finetti's No-Dutch-Book Criterion to Gödel infinite-valued propositional logic.
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  7.  30
    Tarski's theorem on intuitionistic logic, for polyhedra.Nick Bezhanishvili, Vincenzo Marra, Daniel McNeill & Andrea Pedrini - 2018 - Annals of Pure and Applied Logic 169 (5):373-391.
  8.  25
    Gödel algebras free over finite distributive lattices.Stefano Aguzzoli, Brunella Gerla & Vincenzo Marra - 2008 - Annals of Pure and Applied Logic 155 (3):183-193.
    Gödel algebras form the locally finite variety of Heyting algebras satisfying the prelinearity axiom =. In 1969, Horn proved that a Heyting algebra is a Gödel algebra if and only if its set of prime filters partially ordered by reverse inclusion–i.e. its prime spectrum–is a forest. Our main result characterizes Gödel algebras that are free over some finite distributive lattice by an intrisic property of their spectral forest.
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  9.  44
    A Temporal Semantics for Basic Logic.Stefano Aguzzoli, Matteo Bianchi & Vincenzo Marra - 2009 - Studia Logica 92 (2):147-162.
    In the context of truth-functional propositional many-valued logics, Hájek’s Basic Fuzzy Logic BL [14] plays a major rôle. The completeness theorem proved in [7] shows that BL is the logic of all continuous t -norms and their residua. This result, however, does not directly yield any meaningful interpretation of the truth values in BL per se . In an attempt to address this issue, in this paper we introduce a complete temporal semantics for BL. Specifically, we show that BL formulas (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  10.  36
    Algebra and Probability in Many-Valued Reasoning.Ioana Leuştean & Vincenzo Marra - 2010 - Studia Logica 94 (2):147-150.
  11.  25
    A characterization of MV-algebras free over finite distributive lattices.Vincenzo Marra - 2008 - Archive for Mathematical Logic 47 (3):263-276.
    Mundici has recently established a characterization of free finitely generated MV-algebras similar in spirit to the representation of the free Boolean algebra with a countably infinite set of free generators as any Boolean algebra that is countable and atomless. No reference to universal properties is made in either theorem. Our main result is an extension of Mundici’s theorem to the whole class of MV-algebras that are free over some finite distributive lattice.
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark