I'm back in Prague after five days of LOGICA in Hejnice Monastery. I have an overwhelming number of positive things to say about the event: it was flawlessly organised, the content suited my work perfectly, and the social atmosphere is especially outstanding. It's impossible not to enjoy a conference with people like this and a place like Hejnice. I wholeheartedly recommend the conference to everyone.
It's really not easy to choose a couple of talks to mention here, because the conference was packed with interesting topics. It's not often you find yourself at a conference with a whole day dedicated to proof-theoretic semantics. I got my first chance to see Dag Prawitz in action, one of the grand old men of proof-theory. (Proof-theory being a reasonably young discipline, grand old men can be quite young.) His talk was an attempt at giving some epistemic content to the notion of
grounds often used in natural deduction. Ultimately, he wants an integrated story about both validity and grounds that can serve as framework to solve the so-called Carroll-regress problem.
Among other senior people, Schroeder-Heister offered an improvement on the Dummett-Prawitz style proof-theoretic semantics with inductive definitions as the central notion. Logical consequence, he proposes, is relative to a given definition based on clauses of the form A <= B_1, ..., B_n where A is an arbitrary atomic formula and B_1, ..., B_n may be compound. An interesting feature of his proposal is that it can deal with reasoning involving definitions of other things than logical constants. Logical constants is only a special case of particularly well-behaved expressions. The general framework can deal with non-well-founded definitions, and even paradoxical definitions. In fact, together with the fact that tonk is still ruled out by the framework, the connection with Stephen Read's concept of local harmony is quite clear. I'll return to these issues in the future. (Beware: blogosphere promises are vacuous.)
Robert Brandom gave me an opportunity to have a first look into his much discussed
incompatibility semantics. The paper was an exploration of issues discussed in his new book
Between Saying and Doing: Towards an Analytic Pragmatism. The central idea is let a notion of incompatibility serve as a primitive from which logical constants are defined and a logical consequence relation produced. In broad terms, the propositional content of a sentence A is represented by the set of sentences expressing propositions incompatible with A. Perhaps a bit disappointingly, Brandom's semantics seems unavoidably tied up with classical logic. An interesting question is how to tweak the central notion of compatibility (and perhaps structural rules) to acquire incompatibility sematics for non-classical logics. Although Brandom did not have much to offer on this front in the talk, he did have some very interesting things to say about semantics and compositionality. Now, it turns out that his semantics yields a non-compositional semantics for logical connectives. However, Brandom argues that this is not such meaning-theoretic sin after all. For, the semantics is in fact fully recursive, i.e., although the semantics values of logical compounds is not computable from the semantic value of its components, the semantic value of compounds is determined by the semantic values of logically simpler ones.
I'll end here for now. If there is time before I leave again, I'll upload some of the pictures from the conference. Meanwhile, thanks to everyone who participated.
Posts
