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Lukasiewicz and Symmetrical Heyting Algebras

Mathematical Logic Quarterly 23 (7‐12):131-136 (1976)

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An Alternative Definition of Quantifiers on Four-Valued Łukasiewicz Algebras.L. J. González, M. B. Lattanzi & A. G. Petrovich - 2017 - Logica Universalis 11 (4):439-463.details An alternative notion of an existential quantifier on four-valued Łukasiewicz algebras is introduced. The class of four-valued Łukasiewicz algebras endowed with this existential quantifier determines a variety which is denoted by \. It is shown that the alternative existential quantifier is interdefinable with the standard existential quantifier on a four-valued Łukasiewicz algebra. Some connections between the new existential quantifier and the existential quantifiers defined on bounded distributive lattices and Boolean algebras are given. Finally, a completeness theorem for the monadic four-valued (...) Download Export citation Bookmark 1 citation
Completeness theorems via the double dual functor.Adriana Galli, Marta Sagastume & Gonzalo E. Reyes - 2000 - Studia Logica 64 (1):61-81.details The aim of this paper is to apply properties of the double dual endofunctor on the category of bounded distributive lattices and some extensions thereof to obtain completeness of certain non-classical propositional logics in a unified way. In particular, we obtain completeness theorems for Moisil calculus, n-valued Łukasiewicz calculus and Nelson calculus. Furthermore we show some conservativeness results by these methods. Download Export citation Bookmark 1 citation
Proper n-valued łukasiewicz algebras as s-algebras of łukasiewicz n-valued prepositional calculi.Roberto Cignoli - 1982 - Studia Logica 41 (1):3 - 16.details Proper n-valued ukasiewicz algebras are obtained by adding some binary operators, fulfilling some simple equations, to the fundamental operations of n-valued ukasiewicz algebras. They are the s-algebras corresponding to an axiomatization of ukasiewicz n-valued propositional calculus that is an extention of the intuitionistic calculus. Download Export citation Bookmark 11 citations
Symmetrical Heyting algebras with a finite order type of operators.Luisa Iturrioz - 1995 - Studia Logica 55 (1):89 - 98.details The main purpose of this paper is to introduce a class of algebraic structures related to many-valued ukasiewicz algebras. They are symmetrical Heyting algebras with a set of modal operators indexed by a finite completely symmetric poset. A representation theorem is given for these (not functionally complete) algebras. Download Export citation Bookmark
Some Operators in Kripke Models with an Involution.A. Galli & M. Sagastume - 1999 - Journal of Applied Non-Classical Logics 9 (1):107-120.details ABSTRACT In an unpublished paper, we prove the equivalence between validity in 3L-models and algebraic validity in 3-valued Lukasiewicz algebras. R. Cignoli and M. Sagastume de Gallego present in [4] an intrinsic definition of the operators s, for i = 1,…,4 of a 5-valued Lukasiewicz algebra. The aim of the present work is to study those operators in g-Kripke models context and to generalize the result obtained for 3L-models in [9] by proving that there exist g-Kripke models appropriate for 5-valued (...) Download Export citation Bookmark
Algebraic structure of the truth-values for Lω.Alexander S. Karpenko - 1988 - Bulletin of the Section of Logic 17 (3/4):127-133.details This paper is an abstract of the report which was presented on the Polish-Soviet meeting on logic . It is shown that one can consider a lineary-ordered Heyting’s and Brouwer’s algebras as truth-values for Lukasiewicz’s inﬁnite-valued logic’s Lω. Download Export citation Bookmark

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