Sequent calculus for 3-valued paraconsistent logic QMPT0

Abstract

We present a sequent calculus of a paraconsistent logic QMPT0, which has the paraconsistent-type excluded middle law (PEML) as an initial sequent. Our system shows that the presence of PEML is essentially important for QMPT0. It also has special rules when the set of constant symbols is finite. We also discuss the cut-elimination property of our system.