6 found
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  1.  51
    A Geometric Proof of the Completeness of the Łukasiewicz Calculus.Giovanni Panti - 1995 - Journal of Symbolic Logic 60 (2):563-578.
    We give a self-contained geometric proof of the completeness theorem for the infinite-valued sentential calculus of Łukasiewicz.
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  2.  36
    Finitely Generated Free MV-Algebras and Their Automorphism Groups.Antonio Di Nola, Revaz Grigolia & Giovanni Panti - 1998 - Studia Logica 61 (1):65-78.
    The MV-algebra S m w is obtained from the (m+1)-valued ukasiewicz chain by adding infinitesimals, in the same way as Chang's algebra is obtained from the two-valued chain. These algebras were introduced by Komori in his study of varieties of MV-algebras. In this paper we describe the finitely generated totally ordered algebras in the variety MV m w generated by S m w . This yields an easy description of the free MV m w -algebras over one generator. We characterize (...)
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  3.  69
    Varieties of MV-Algebras.Giovanni Panti - 1999 - Journal of Applied Non-Classical Logics 9 (1):141-157.
    ABSTRACT We characterize, for every subvariety V of the variety of all MV- algebras, the free objects in V. We use our results to compute coproducts in V and to provide simple single-axiom axiomatizations of all many-valued logics extending the Lukasiewicz one.
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  4.  14
    Decidable and Undecidable Prime Theories in Infinite-Valued Logic.Daniele Mundici & Giovanni Panti - 2001 - Annals of Pure and Applied Logic 108 (1-3):269-278.
    In classical propositional logic, a theory T is prime iff it is complete. In Łukasiewicz infinite-valued logic the two notions split, completeness being stronger than primeness. Using toric desingularization algorithms and the fine structure of prime ideal spaces of free ℓ -groups, in this paper we shall characterize prime theories in infinite-valued logic. We will show that recursively enumerable prime theories over a finite number of variables are decidable, and we will exhibit an example of an undecidable r.e. prime theory (...)
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  5.  25
    Generic Substitutions.Giovanni Panti - 2005 - Journal of Symbolic Logic 70 (1):61-83.
    Up to equivalence, a substitution in propositional logic is an endomorphism of its free algebra. On the dual space, this results in a continuous function, and whenever the space carries a natural measure one may ask about the stochastic properties of the action. In classical logic there is a strong dichotomy: while over finitely many propositional variables everything is trivial, the study of the continuous transformations of the Cantor space is the subject of an extensive literature, and is far from (...)
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  6. Measures Induced by Units.Giovanni Panti & Davide Ravotti - 2013 - Journal of Symbolic Logic 78 (3):886-910.
    The half-open real unit interval an automorphism-invariant positive normalized linear functional onH. SinceHis representable as a uniformly dense set of continuous functions on its maximal spectrum, such functionals—in this context usually called states—amount to automorphism-invariant finite Borel measures on the spectrum. Different choices for the unit may be algebraically unrelated, but our second main result shows that the corresponding measures are always absolutely continuous w.r.t. each other, and provides an explicit expression for the reciprocal density.
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