AN INFORMATIONAL SEMANTICS FOR LOGICAL CONSEQUENCE

Abstract

In semantic terms, the logical consequence is usually defined from the truth value of the premises and conclusion: this is true in every situation in which the former are true. It can be understood that, in these cases, the conclusion does not contain more information than the set of premises. Based on this idea, we develop, in this article, a definition of informational logical consequence, based on the notion of information suggested in the Mathematical Theory of Communication. We show some results, such as that, despite being inconsistent, the system underlying this notion is not trivial and that the logic underlying the informational logical consequence is not classical, but some kind of paraconsistent logic.