Paraconsistent Logic
Graham Priest · 2002
Abstract This chapter provides the details of the paraconsistent logic to be used in the construction of a mereological theory of nothing(ness). A logic is paraconsistent if it is one in which Explosion is not valid. (Explosion is the inference: for all $A$ and $B$: $A,\lnot A\vdash B$.) Such a logic allows for inconsistent theories where the inconsistencies are kept strictly under control. The logic used is first-order $LP$, augmented with an appropriate conditional connective. When this conditional is used to define a contraposible conditional, this gives the logic $RM_{3}$. The chapter explains the semantics of this logic and then specifies appropriate proof theories (both axiomatic and tableau-theoretic) for it. The chapter ends by discussing briefly the addition of the machinery of the $\varepsilon$-calculus to the logic.