Dynamic Łukasiewicz logic and its application to immune system
Antonio Di Nola, Revaz Grigolia, Nunu Mitskevich, Gaetano Vitale · Soft Computing · 2021
Abstract It is introduced an immune dynamicn-valued Łukasiewicz logic $$ID{\L }_n$$ IDŁn on the base ofn-valued Łukasiewicz logic $${\L }_n$$ Łn and corresponding to it immune dynamic $$MV_n$$ MVn -algebra ( $$IDL_n$$ IDLn -algebra), $$1< n < \omega $$ 1<n<ω , which are algebraic counterparts of the logic, that in turn represent two-sorted algebras $$(\mathcal {M}, \mathcal {R}, \Diamond )$$ (M,R,◊) that combine the varieties of $$MV_n$$ MVn -algebras $$\mathcal {M} = (M, \oplus , \odot , \sim , 0,1)$$ M=(M,⊕,⊙,∼,0,1) and regular algebras $$\mathcal {R} = (R,\cup , ;, ^*)$$ R=(R,∪,;,∗) into a single finitely axiomatized variety resemblingR-module with “scalar” multiplication $$\Diamond $$ ◊ . Kripke semantics is developed for immune dynamic Łukasiewicz logic $$ID{\L }_n$$ IDŁn with application in immune system.