Modality and Paraconsistency
João Marcos · 2005
Paraconsistent logic was born in the vicinity of modal logic. Moreover, as every other non-classical logicians, paraconsistentists have very often flirted with modalities. The first known system of paraconsistent logic was in fact defined as a fragment of S5, in the late 40s. But a fragment of a modal system is not necessarily a modal system. I will show here, indeed, that Ja´skowski’s D2 is not a modal logic, in the contemporary usual meaning of the term. By contrast, I will also show, subsequently, that any non-degenerate normal modal system is inherently paraconsistent. 1 What is a paraconsistent logic? Classical logic is maculated by many irrelevancies. The enterprise of paraconsistency was designed so as to help cleansing a particular stain, by eschewing the so-called Principle of Explosion: (PE) ∀α∀β(α, ¬α ⊩ β). According to (PE), contradictions are malicious creatures: Whenever they are