Jean-Yves BÃ©ziau (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.
Luca ViganÃ² (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: AâˆªB 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 â€œhistoryâ€ of until, i.e., the â€œinternalâ€ universal quantification over the time instants between the current one and wâ€². 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.