Dynamic Łukasiewicz logic and its application to immune system

Abstract It is introduced an immune dynamic n -valued Łukasiewicz logic $$ID{\L }_n$$ IDŁn on the base of $${\L xmlns:mml="http://www.w3.org/1998/Math/MathML">Łn and corresponding to it $$MV_n$$ xmlns:mml="http://www.w3.org/1998/Math/MathML">MVn -algebra ( $$IDL_n$$ xmlns:mml="http://www.w3.org/1998/Math/MathML">IDLn -algebra), $$1< < \omega $$ xmlns:mml="http://www.w3.org/1998/Math/MathML">1<n<ω , which are algebraic counterparts logic, that in turn represent two-sorted algebras $$(\mathcal {M}, \mathcal {R}, \Diamond )$$ xmlns:mml="http://www.w3.org/1998/Math/MathML">(M,R,◊) combine varieties -algebras $$\mathcal {M} = (M, \oplus \odot \sim 0,1)$$ xmlns:mml="http://www.w3.org/1998/Math/MathML">M=(M,⊕,⊙,∼,0,1) regular {R} (R,\cup ;, ^*)$$ xmlns:mml="http://www.w3.org/1998/Math/MathML">R=(R,∪,;,∗) into a single finitely axiomatized variety resembling R -module with “scalar” multiplication $$\Diamond xmlns:mml="http://www.w3.org/1998/Math/MathML">◊ . Kripke semantics developed for application system.