Department of Philosophy and Science Studies
University of Roskilde
Thursday 13 June 2013, 16.15 until 17.45,
Munich Center for Mathematical Philosophy (MCMP)
I will be the first to admit that this title is unlikely to set anyone's pulse racing. Problems in modal deduction? What is hybrid logic anyway? And why should anyone care?
Fair questions, and ones I will tackle in the talk. In essence, I will be sketching an overview of why modal deduction is tricky, and why hybrid logic fixes (some of) its problems. Themes I will emphasize include the second-order nature of modal logic, how hybrid logic yields a first-order perspective on frame structure, and how ''non-standard'' hybrid inference rules turn out to be sequent rules ''missing'' from orthodox modal logic, and completeness via Henkin constructions.
And there is a cherry on the cake. If I had given this talk even five weeks ago, I would have concluded by saying that basic hybrid deduction is now well understood. Well, it turns out there is more to be said, and (time permitting) I shall close the talk by mentioning some very recent joint work with Thomas Bolander, Torben Braüner, and Klaus Frovin Jørgensen on what we term Seligman-style tableaux, in honour of classic (but somewhat overlooked) work by Jerry Seligman dating back to the 1990s on hybrid deduction.
I intend to make the talk relatively self contained and won't presuppose any particular expertise in modal (let alone hybrid) logic. But for those of you who who would like to do some reading in advance, here are some suggestions:
Hybrid Logic, Chapter 7, Section 3 of Modal Logic, by Patrick Blackburn, Maarten de Rijke, and Yde Venema, Cambridge University Press, 2001, pages 434-445.
Pure Extensions, Proof Rules, and Hybrid Axiomatics, by Patrick Blackburn and Balder ten Cate, Studia Logica, volume 84, pages 277-322, 2006.
Internalisation: The Case of Hybrid Logics, by Jerry Seligman, Journal of Logic and Computation, volume 11, pages 671-689, 2001.