Fraïssé’s theorem for logics of formal inconsistency

Abstract

Abstract We prove that the minimal Logic of Formal Inconsistency (LFI) $\mathsf{QmbC}$ (basic quantified logic of formal inconsistency) validates a weaker version of Fraïssé’s theorem (FT). LFIs are paraconsistent logics that relativize the Principle of Explosion only to consistent formulas. Now, despite the recent interest in LFIs, their model-theoretic properties are still not fully understood. Our aim in this paper is to investigate the situation. Our interest in FT has to do with its fruitfulness; the preservation of FT indicates that a number of other classical semantic properties can be also salvaged in LFIs. Further, given that FT depends on truth-functionality (a property that, in general, fails in LFIs), whether full FT holds for $\mathsf{QmbC}$ becomes a challenging question.