Immune Logics

Abstract

This article is concerned with an exploration of a family of systems---called immune logics---whose main properties are, in some sense, related to those of the well-known family of infectious logics. The distinctive feature of the semantic of infectious logics is the presence of a certain ``infectious´´ semantic value, i.e. a value which is a zero element for all the operations in the underlying algebraic structure. On the other hand, what is characteristic of the semantic of immune logics is to have a certain ``immune´´ value, i.e. an identity element for the binary operations in the underlying algebraic structure. In this article, we will define these structures, focusing on the 3-element case, discuss the relations between immune and infectious elements, and provide technical results regarding them, and the various logical systems defined using such semantics.