Notre Dame Journal of Formal Logic

Ways Things Can't Be

Greg Restall


Paraconsistent logics are often semantically motivated by considering "impossible worlds." Lewis, in "Logic for equivocators," has shown how we can understand paraconsistent logics by attributing equivocation of meanings to inconsistent believers. In this paper I show that we can understand paraconsistent logics without attributing such equivocation. Impossible worlds are simply sets of possible worlds, and inconsistent believers (inconsistently) believe that things are like each of the worlds in the set. I show that this account gives a sound and complete semantics for Priest's paraconsistent logic LP, which uses materials any modal logician has at hand.

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Notre Dame J. Formal Logic Volume 38, Number 4 (1997), 583-596.

First available in Project Euclid: 10 December 2002

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Zentralblatt MATH identifier

Primary: 03B53: Paraconsistent logics
Secondary: 03A05: Philosophical and critical {For philosophy of mathematics, see also 00A30} 03B45: Modal logic (including the logic of norms) {For knowledge and belief, see 03B42; for temporal logic, see 03B44; for provability logic, see also 03F45}


Restall, Greg. Ways Things Can't Be. Notre Dame J. Formal Logic 38 (1997), no. 4, 583--596. doi:10.1305/ndjfl/1039540771.

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