Team Parsifal

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Section: New Results

A game semantics for proof search

An exciting area of foundational work is to establish connections between the proof search paradigm and the recent work on game semantics , on ludics [26] , and the general and rather old notions of logic and interaction . Using these ideas might allow us to take a neutral approach to proof and refutation: that is, one does some kind of computation with logical expressions and when finished, one finds out if one has a proof or a refutation. For example, consider asking Prolog the query G: if Prolog returns saying ``yes'', we can claim that Prolog has found a proof. If Prolog returns saying ``no'', then we would normally say that it has failed to find a proof of G. In fact, given some insights from LINC, it is, in fact, possible to say in the latter case (that is, in the finite failure case), that Prolog actually constructed a proof of ¬ G . This fundamental duality between success and failure has always been a challenge to traditional proof search and proof theory. Alexis Saurin and Miller [12] have provided a game theoretic foundations for various interesting and computationally useful subsets of linear logic. For example, proof search with the usual specification for bisimulation is assigned the usual game theoretical semantics.


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