Information, negation, and paraconsistency

Abstract

This paper begins by arguing that a truth conditional approach to the semantics for relevant logic is unnatural. Rather, we should adopt an informational semantics. On this view, the indices in the model theory are not possible or impossible worlds, but are situations. A statement is not true or false at a situation; rather a situation can be said either to contain or fail to contain certain pieces of information. Valid inference, then, is seen as information preservation, not truth preservation. The distinction between truth and information gives us some freedom in our treatment of logic. For example, we may have a very classical theory of truth but a very non-classical theory of information. On the other hand, we may accept very non-classical theories of truth (such as dialetheism) together with an informational treatment of logic.