Focusing in Asynchronous Games

14 years 3 months ago

Download www.pps.jussieu.fr

Game semantics provides an interactive point of view on proofs, which enables one to describe precisely their dynamical behavior during cut elimination, by considering formulas as games on which proofs induce strategies. We are speciﬁcally interested here in relating two such semantics of linear logic, of very diﬀerent ﬂavor, which both take in account concurrent features of the proofs: asynchronous games and concurrent games. Interestingly, we show that associating a concurrent strategy to an asynchronous strategy can be seen as a semantical counterpart of the focusing property of linear logic. A cut-free proof in sequent calculus, when read from bottom up, progressively introduces the connectives of the formula that it proves, in the order speciﬁed by the syntactic tree constituting the formula, following the conventions induced by the logical rules. In this sense, a formula can be considered as a playground that the proof will explore. The formula describes the rules that th...

Samuel Mimram

Real-time Traffic