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Pure alethic modal logics

on 12-02-2010

... Jean-Yves Béziau (UFC/CNPq/FUNCAP, U Fortaleza, Brazil).

February 12, 2010, Friday, 16h15m.

Abstract: In this talk I will present systems of pure modal logics, i.e. with modalities as only connectives. I will focus on alethic modalities: necessity and possibility. The basic framework is structural conesquence relation in the sense of Los and Susko. I will study the main options and present bivalent and multi-valued semantics for these systems as well as sequent-calculi.
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A HIstory of Until

on 10-02-2010

... Luca Viganò (U Verona, Italy).

February 10, 2010, Wednesday, 15h30m.

Abstract: Until is a notoriously difficult temporal operator as it is both existential and universal at the same time: A∪B holds at the current time instant w iff either B holds at w or there exists a time instant w’ in the future at which B holds and such that A holds in all the time instants between the current one and w’. This "ambivalent"t; nature poses a significant challenge when attempting to give deduction rules for until. In this paper, in contrast, we make explicit this duality of until by introducing a new temporal operator that allows us to formalize the “history” of until, i.e., the “internal” universal quantification over the time instants between the current one and w′. This approach provides the basis for formalizing deduction systems for temporal logics endowed with the until operator. For concreteness, we give here a labeled natural deduction system for a linear-time logic endowed with the new history operator and show that, via a proper translation, such a system is also sound and complete with respect to the linear temporal logic LTL with until. Reporting on joint work with Andrea Masini and Marco Volpe.

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