A cartography of LFIs and truth

Abstract

The goal of this paper is to offer an initial taxonomy of the LFIs (logics of formal inconsistency) and that can be non-trivially extended with a transparent truth predicate. To fulfill this task, we take a semantic point of view. We define two families of logics: infectious logics (obtained as a generalization of the semantic behavior present in the {¬, ∧, ∨}-fragment of logics of nonsense) and non-infectious logics (i.e. logics that are not infectious). Using two paradigmatic logics of each kind, we generate an extensive collection of non-classical logics –some of which have been discussed in the literature and many that have not– and consider the prospect of extending them with a consistency operator and a truth predicate. We show that, when extended in this way, most of the non-infectious systems are trivial and that all the infectious ones are non-trivial. To complete the analysis, we provide philosophical reasons for being interested in the logics of formal inconsistency and truth introduced in this paper.