Immune Logics

SZMUC, DAMIÁN ENRIQUE

Paris

Seminario; Linguae Seminar; 2020

Ecole Normale Superieur - Institute Jean Nicod

In the past few years, the family of many-valued logics called infectious logics received an increasing amount of attention. These systems count with a truth-value that is assigned to a complex formula whenever it is assigned to some of its components---thus, behaving in an infectious way. Rather informally, we could say that these values behave in a "value-in-value-out" fashion. From a mathematical point of view, infectious values of this sort can be thought of as all-purpose zero elements. The aim of this talk is to discuss a family of many-valued logics that can perhaps be considered as duals to the infectious systems---whence, they will be called immune logics. In this vein, these logics count with a truth-value that is never assigned to a complex formula whenever it is assigned to some of its components, except in certain cases. Once again rather informally, we could say that in some of these cases these values behave in a "value-in-different-value-out" manner. Therefore, immune values of this sort can be thought of as all-purpose identity elements. As regards immune logics, our goal is to describe and analyze various three-valued systems. For this purpose, we explore immune logics where validity is defined by letting the immune value be designated, systems where it is undesignated, and systems where mixed notions of validity are adopted. In doing so, we highlight the links to various logics that have already appeared in the literature and some which were not discussed until now.