Dynamic Łukasiewicz logic and its application to immune system

It is introduced an immune dynamic n-valued Łukasiewicz logic $$ID{\L }_n$$ on the base of n-valued Łukasiewicz logic $${\L }_n$$ and corresponding to it immune dynamic $$MV_n$$ -algebra ( $$IDL_n$$ -algebra), $$1< n < \omega $$ , which are algebraic counterparts of the logic, that in turn represent two-sorted algebras $$(\mathcal {M}, \mathcal {R}, \Diamond )$$ that combine the varieties of $$MV_n$$ -algebras $$\mathcal {M} = (M, \oplus , \odot , \sim , 0,1)$$ and regular algebras $$\mathcal {R} = (R,\cup , ;, ^*)$$ into a single finitely axiomatized variety resembling R-module with “scalar” multiplication $$\Diamond $$ . Kripke semantics is developed for immune dynamic Łukasiewicz logic $$ID{\L }_n$$ with application in immune system.