- The lack of disagreement on the proper set of structural rules for intuitionistic logic (cf. the wildly different approaches of, e.g., Felscher and Rahman).
- The problem, illustrated by N, of the interplays that arise in sets of independently plausible structural rules.
- Difficulties in identifying acceptable criteria which allow us to rule out particle rules for connectives like tonk, but which do not force us to rule out, e.g., the particle rules for negation.
Tuesday, March 29, 2011
Tuesday, March 1, 2011
I presented the result (joint with Sara and Aleks Knoks, whom we snagged to work on dialogues with us) on an extension of what I've been calling Fermüller-style dialogue games to classical logic. Fermüller gave a nice presentation of a dialogue game for intuitionistic logic, and presented a proof of the soundness and completeness of his games in his “Parallel Dialogue Games and Hypersequents for Intermediate Logics” (which was discussed earlier [Part 1], [Part 2], [Part 3], [Part 4]). Chris Fermüller was at the workshop and attended my talk. He didn't much like the name “Fermüller-style dialogues”, the idea being that his dialogues are at most a notational variant of ordinary dialogue games. I defended the choice of term by pointing out that the idea of extending his intuitionistic games to classical logic was more attractive and feasible than it is for other formalisms for dialogues. I think this is a case where a change of notation is significant.
As I expected, there was some pushback at the basic motivation of the paper, which is that our result is worthwhile owing to the extremely small number of explicit proofs in the dialogue literature of the correspondence between classical logic and classical dialogues (in whatever form one likes). We know of only two proofs, one by Fermüller himself, and another by Sørensen and Urzyczyn. Our proof has the advantage that it works with a standard sequent calculus, rather than with hypersequents (Fermüller) or one that is specially tuned for the purpose of establishing the correspondence (Sørensen and Urzyczyn).
It was an honor to present the work to an audience that contained several experts on dialogical logic. Here are the slides. The presentation was rather less than ideal: there were so many talks on dialogues preceding mine (not to mention that Fermüller himself presented his games immediately before me) that the first several slides could have been cut, and other interesting issues from the paper could have been dealt with. The paper on which the slides are based can be found on Sara's homepage or on my homepage.