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 DPŁ (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 DPŁ ( 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 DPŁ ( 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 ).

中文翻译：

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动态 Łukasiewicz 逻辑和动态 MV 代数

摘要 继 K. Segerberg [22]、D. Kozen [15] 和 V. Pratt [19] 之后，他们介绍了动态命题逻辑和动态代数，动态命题 Łukasiewicz 逻辑 DPŁ（动态 n 值命题 Łukasiewicz 逻辑 DP Ł n ) 和动态 MV-代数 (dynamic MV n -algebras) 和逻辑 DPŁ ( DP Ł n ) 和动态 MV-代数 (MV n -algebras) 的理论得到发展。动态 MV-代数 (dynamic MV n -algebras) 是逻辑 DPŁ ( DP Ł n ) 的代数对应物，它们又代表二分类代数，它们结合了 MV-代数 (MV n -algebras) ( M , ⊕ , ⊙ , ∼ , 0 , 1 ) 和正则代数 ( R , ∪ , ; , ⁎ ) 变成一个单一的有限公理化变体 ( M , R , ◇ )，类似于带有“标量”乘法的 R 模 ◇。