Uniform labelled calculi for preferential conditional logics based on neighbourhood semantics

International audienceThe preferential conditional logic PCL, introduced by Burgess, and its extensions are studied. First, a natural semantics based on neighbourhood models, which generalise Lewis' sphere models for counterfactual logics, is proposed. Soundness and completeness of PCL and its extensions with respect to this class of models are proved directly. Labelled sequent calculi for all logics of the family are then introduced. The cal-culi are modular and have standard proof-theoretical properties, the most important of which is admissibility of cut, that entails a syntactic proof of completeness of the calculi. By adopting a general strategy, root-first proof search terminates, thereby providing a decision procedure for PCL and its extensions. Finally, the semantic completeness of the calculi is established: from a finite branch in a failed proof attempt it is possible to extract a finite countermodel of the root sequent. The latter result gives a constructive proof of the finite model property of all the logics considered

In Search of an Integrated Logic of Conviction and Intention

According to a two-level criterion for combination tests in the field of ordinary language (C-CT), moral 'ought'-sentences may be taken to imply 'I intend'-sentences partly semantically and partly pragmatically. If so, a trenchant linguistic analysis of the concept of moral obligation cannot do without a non-classical logic which allows to model these important kinds of ordinary-language implications by means of purely syntactical derivations. For this purpose, an integrated logic of conviction and intention has been tentatively devised by way of a doxastically, buletically, and pragmatically extended calculus of natural deduction. This system of buletic logic cannot even be launched without one or two derivation rules of deductive closedness. However, these very closedness rules appear to be responsible for buletic paradoxes which are analogous to paradoxes long since known from other, less exotic branches of logic but at first sight look much more virulent. After having scrutinized two potential strategies for coping with the paradoxes of buletic logic, finally we can convince ourselves that these paradoxes, as well as their familiar non-buletic counterparts, are but apparent paradoxes, provided we consistently lean on C-CT and do not let pragmatical considerations intrude into purely logical ones

Modal homotopy type theory

Chapter IV of a book which looks to demonstrate what philosophy can gain from the new formal language of modal homotopy type theory. Here I explore how we should understand the addition of modalities to homotopy type theory. This chapter will sit between modified versions of http://philsci-archive.pitt.edu/13448/ and http://philsci-archive.pitt.edu/11809/