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Your search keyword '"KRIPKE semantics"' showing total 6 results
6 results on '"KRIPKE semantics"'

1. Dynamic Łukasiewicz Logic and Dynamic MV-algebras.

Author

Di Nola, Antonio, Grigolia, Revaz, and Vitale, Gaetano

Subjects
*KRIPKE semantics, *MATHEMATICAL logic, *ALGEBRAIC logic, *LOGIC, *ALGEBRA
Abstract

Following K. Segerberg [22] , D. Kozen [15] and V. Pratt [19] , who have been introduced dynamic propositional logic and dynamic algebras, dynamic propositional Łukasiewicz logic DP Ł (dynamic n -valued propositional Łukasiewicz logic D P Ł n) and dynamic MV -algebras (dynamic M V n -algebras) are introduced and theories of the logic DP Ł (D P Ł n) and dynamic MV -algebras (M V n -algebras) are developed. Dynamic MV -algebras (dynamic M V n -algebras) are algebraic counterparts of the logic DP Ł (D P Ł n), that in turn represent two-sorted algebras that combine the varieties of MV -algebras (M V n -algebras) (M , ⊕ , ⊙ , ∼ , 0 , 1) and regular algebras (R , ∪ , ; , ⁎) into a single finitely axiomatized variety (M , R , ◇) resembling R -module with "scalar" multiplication ◇. Kripke semantics is developed for dynamic propositional Łukasiewicz logic (dynamic n -valued propositional Łukasiewicz logic D P Ł n). [ABSTRACT FROM AUTHOR]

Published
2020
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2. DISTRIBUTED RELATION LOGIC.

Author

Allwein, Gerard, Harrison, William L., and Reynolds, Thomas

Subjects
BOOLEAN algebra, RELATION algebras, RELEVANCE logic, KRIPKE semantics, ALGEBRAIC logic
Abstract

We extend the relational algebra of Chin and Tarski so that it is multisorted or, as we prefer, typed. Each type supports a local Boolean algebra outfitted with a converse operator. From Lyndon, we know that relation algebras cannot be represented as proper relation algebras where a proper relation algebra has binary relations as elements and the algebra is singly-typed. Here, the intensional conjunction, which was to represent relational composition in Chin and Tarski, spans three different local alge- bras, thus the term distributed in the title. Since we do not rely on proper relation algebras, we are free to re-express the algebras as typed. In doing so, we allow many different intensional conjunction operators. We construct a typed logic over these algebras, also known as heterogeneous algebras of Birkhoff and Lipson. The logic can be seen as a form of relevance logic with a classical negation connective where the Routley-Meyer star operator is reified as a converse connective in the logic. Relevance logic itself is not typed but our work shows how it can be made so. Some of the properties of classical relevance logic are weakened from Routley-Meyer's version which is too strong for a logic over relation algebras. [ABSTRACT FROM AUTHOR]

Published
2017
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3. Basic Core Fuzzy Logics and Algebraic Routley–Meyer-Style Semantics.

Author

Yang, Eunsuk

Subjects
*ALGEBRAIC logic, *SEMANTICS, *KRIPKE semantics, *LOGIC
Abstract

Recently, algebraic Routley–Meyer-style semantics was introduced for basic substructural logics. This paper extends it to fuzzy logics. First, we recall the basic substructural core fuzzy logic MIAL (Mianorm logic) and its axiomatic extensions, together with their algebraic semantics. Next, we introduce two kinds of ternary relational semantics, called here linear Urquhart-style and Fine-style Routley–Meyer semantics, for them as algebraic Routley–Meyer-style semantics. [ABSTRACT FROM AUTHOR]

Published
2021
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4. Fuzzy Topology and Łukasiewicz Logics from the Viewpoint of Duality Theory

Author

Yoshihiro Maruyama

Subjects
compactness theorem, Mathematics::General Mathematics, Logic, Duality (mathematics), fuzzy topology, many-valued logic, MV-algebra, Stone duality, Fuzzy logic, Jónsson-Tarski duality, Algebra, algebraic logic, Interior algebra, History and Philosophy of Science, Monoidal t-norm logic, Computer Science::Logic in Computer Science, ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION, T-norm fuzzy logics, Łukasiewicz logic, Mathematics, modal logic, Kripke semantics
Abstract

This paper explores relationships between many-valued logic and fuzzy topology from the viewpoint of duality theory. We first show a fuzzy topological duality for the algebras of Łukasiewicz n-valued logic with truth constants, which generalizes Stone duality for Boolean algebras to the n-valued case via fuzzy topology. Then, based on this duality, we show a fuzzy topological duality for the algebras of modal Łukasiewicz n-valued logic with truth constants, which generalizes Jonsson-Tarski duality for modal algebras to the n-valued case via fuzzy topology. We emphasize that fuzzy topological spaces naturally arise as spectrums of algebras of many-valued logics.

Published
2010

6. A unifying theorem for algebraic semantics and dynamic logics

Author

Hajnal Andréka, István Németi, Irène Guessarian, Laboratoire d'informatique Algorithmique : Fondements et Applications (LIAFA), Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), and Guessarian, Irene

Subjects
Correctness, Computer science, Semantics (computer science), 02 engineering and technology, 0102 computer and information sciences, 01 natural sciences, Theoretical Computer Science, Monoidal t-norm logic, Computer Science::Logic in Computer Science, ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION, 0202 electrical engineering, electronic engineering, information engineering, 0101 mathematics, Algebra over a field, Principle of bivalence, Mathematics, Discrete mathematics, Mathematical logic, Classical logic, 010102 general mathematics, Ultraproduct, 16. Peace & justice, Algebraic logic, Computer Science Applications, Algebra, TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES, Algebraic semantics, Computational Theory and Mathematics, 010201 computation theory & mathematics, Computer Science::Programming Languages, 020201 artificial intelligence & image processing, Kripke semantics, T-norm fuzzy logics, Partially ordered set, Information Systems
Abstract

A unified single proof is given which implies theorems in such diverse fields as continuous algebras of algebraic semantics, dynamic algebras of logics of programs, and program verification methods for total correctness. The proof concerns ultraproducts and diagonalization.

Published
1987

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