出版社：Philosophy Department, University of Melbourne
摘要：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.
其他摘要：This article is concerned with an exploration of a family of systems—called immune logics—that arise from certain dualizations 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, by which two different though equivalent things are meant. On the one hand, it is meant that these values are zero elements for all the operations in the underlying algebraic structure. On the other hand, it is meant that these values behave in a value-in-value-out fashion for all the operations in the underlying algebraic structure. Thus, in a rather informal manner, we will refer to immune logics as those systems whose underlying semantics count with a certain “immune” semantic value behaving in a way that is somewhat dual to that of the infectious values. In a more formal manner, carrying out this dualization will prove to be not as straightforward as one could imagine, since the two characterizations of infectiousness discussed above lead to two different outcomes when one tries to conduct them. We explore these alternatives and provide technical results regarding them, and the various logical systems defined using such semantics.
