* The author is a Postdoctoral Fellow of the Special Research Fund of Ghent University. I'm indebted to Diderik Batens and Joke Meheus for helpful suggestions that significantly improved the logics presented in this paper. Moreover, I also wish to thank the anonymous referees for pointing out some unclarities in a previous version of this paper, as well as Bert Leuridan for his suggestions on how to state things more clearly. Of course, all remaining unclarities are mine.
In this paper, I will show that it is possible to delete Ex Falso Quodlibet from Classical Logic, without depriving it of any of its deductive powers. This is done by means of the ambiguity-adaptive logic AAL ns , which is equivalent to dCR, the deductive version of Neil Tennant's CR.
In this paper, I will characterize a new class of inconsistencyadaptive logics, namely inconsistency-adaptive modal logics. These logics cope with inconsistencies in a modal context. More specifically, when faced with inconsistencies, inconsistency-adaptive modal logics avoid explosion, but still allow the derivation of sufficient consequences to adequately explicate the part of human reasoning they are intended for.As adaptive logics (AL) include, but are not restricted to inconsistencyadaptive logics (a common misunderstanding about adaptive logics), I will first give a characterization of AL in general. Next, I will turn to inconsistency-adaptive logics in particular. The former will be done by presenting the standard format of AL (see also [3,5]), the latter by specifying how inconsistency-adaptive logics fit the standard format of AL (see also [1,2,9]).The Standard Format. All (standard) adaptive logics are fully characterized by three elements: a lower limit logic (LLL), a set of abnormalities Ω (a set of formulas characterized by a logical form F), and an adaptive strategy.The LLL is the stable part of an adaptive logic, which comes down to the fact that all LLL-consequences of a premise set are also ALconsequences of that premise set. Proof theoretically, this means that in AL-proofs, all LLL-inference rules may be applied unrestrictedly.
Hearers get at the intended meaning of uncooperative utterances (i.e. utterances that conflict with the prescriptions laid down by the Gricean maxims) by pragmatically deriving sentences that reconcile these utterances with the maxims. Such pragmatic derivations are made according to pragmatic rules called implicatures. As they are pragmatic in nature, the conclusions drawn by applying implicatures remain uncertain. In other words, they may have to be withdrawn in view of further information. Because of this last feature, Levinson argued that implicatures should be formally modeled as non-monotonic or default rules of inference. In this paper, I will do exactly this: by relying on the Adaptive Logics Programme, I will provide a formal explication of implicatures as default inference rules. More specifically, I will do so for a particular kind of implicatures, viz scalar implicatures.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.