True and False: An Exchange

in G. Priest, J. C. Beall, and B. Armour-Garb (eds.), The Law of Non-Contradiction. New Philosophical Essays, Oxford, Oxford University Press, 2004

Mind, 2009

2009

The present contribution might be regarded as a kind of defense of the common sense in logic. It is demonstrated that if the classical negation is interpreted as the minimal negation with n = 2 truth values, then deviant logics can be conceived as extension of the classical bivalent frame. Such classical apprehension of negation is possible in non- classical logics as well, if truth value is internalized and bivalence is replaced by bipartition.

Journal of Logic Programming, 1998

The class of logic programs with negation as failure in the head is a subset of the logic of MBNF introduced by Lifschitz and is an extension of the class of extended disjunctive programs. An interesting feature of such programs is that the minimality of answer sets does not hold. This paper considers the class of general extended disjunctive programs (GEDPs) as logic programs with negation as failure in the head. First, we discuss that the class of GE-DPs is useful for representing knowledge in various domains in which the principle of minimality is too strong. In particular, the class of abductive programs is properly included in the class of GEDPs. Other applications include the representation of inclusive disjunctions and circumscription with fixed predicates. Secondly, the semantic nature of GEDPs is analyzed by the syntax of programs. In acyclic programs, negation as failure in the head can be shifted to the body without changing the answer sets of the program. On the other hand, supported sets of any program are always preserved by the same transformation. Thirdly, the computational complexity of the class of GEDPs is shown to remain in the same complexity class as normal disjunctive programs. Through the simulation of negation as failure in the head, computation of answer sets and supported sets is realized using any proof procedure for extended or positive disjunctive programs. Finally, a simple translation of GEDPs into autoepistemic logic is presented.

In certain languages, disjunctions exhibit PPI behavior (cf. Szabolcsi ):

Canadian Journal of Philosophy, 1998

The validity of argument by disjunctive syllogism (henceforth, DS) has been denied by proponents of relevant and paraconsistent logic (who are sometimes one and the same). DS is stigmatised for its role in inferences — most notably C.I. Lewis's derivation of that fallacy of irrelevance ex falso quodlibet (EFQ) — that involve both it and other rules of inference governing disjunction, or, to speak more precisely, other rules of inference taken to apply to the very same disjunction that obeys DS. In avoiding these inferences the road less travelled is to deny the identity rather than to deny DS: what follows is, then, an exercise in disjoining disjunctions.

Semantics and Pragmatics, 2010

In this extended commentary I discuss the problem of how to account for "conjunctive" readings of some sentences with embedded disjunctions for globalist analyses of conversational implicatures. Following Franke (2010, 2009), I suggest that earlier proposals failed, because they did not take into account the interactive reasoning of what else the speaker could have said, and how else the hearer could have interpreted the (alternative) sentence(s). I show how Franke's idea relates to more traditional pragmatic interpretation strategies.

Linguistics and Philosophy, 2008

2006 in Malaga, Spain. I owe a special thanks to Noam Chomsky for detailed comments at a time when his attention was much needed elsewhere. I am most indebted to the following teachers and colleagues for the extreme generosity with which they gave of their time, comments, and criticisms: Kai von Fintel, Danny Fox, Irene Heim, Roni Katzir and Bob Stalnaker. I must also thank the Social Sciences and Humanities Research Council of Canada for their support (Number 752-2004-0542.

Journal of Philosophical Logic, 2012

Naive speakers find some logical contradictions acceptable, specifically borderline contradictions involving vague predicates such as Joe is and isn't tall. In a recent paper, Cobreros et al. (Journal of Philosophical Logic 2011) suggest a pragmatic account of the acceptability of borderline contradictions. We show, however, that the pragmatic account predicts the wrong truth conditions for some examples with disjunction. As a remedy, we propose a semantic analysis instead. The analysis is close to a variant of fuzzy logic, but conjunction and disjunction are interpreted as intensional operators.