1. Dynamic Łukasiewicz Logic and Dynamic MV-algebras.
- Author
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Di Nola, Antonio, Grigolia, Revaz, and Vitale, Gaetano
- Subjects
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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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