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SUMMARY:Logics for Coalgebras - Alexander Kurz\, University of Leicester
DTSTART:20071130T140000Z
DTEND:20071130T150000Z
UID:TALK8356@talks.cam.ac.uk
CONTACT:Sam Staton
DESCRIPTION:Coalgebras for a functor _F_ generalize transition systems. Us
 ing techniques from category theory\, it is possible to study different cl
 asses of transition systems uniformly in the parameter _F_. Coalgebraic lo
 gic aims at extending this uniform approach to logics of transition system
 s. In this talk\, we will address the question how to associate to any set
 -functor _F_ a corresponding logic\, together with a complete calculus. Th
 is can be achieved by associating to each _F_ a `dual' functor _L_ on Bool
 ean algebras\, which encodes a modal logic for _F_-coalgebras.\n\nThis fun
 ctorial view of a modal logic leads to an elegant abstract\naccount of mod
 al logics for transition systems\, which we will review in this talk. In p
 articular: a) In order to explain the relationship\nbetween a functor _L_ 
 and its modal logic\, we introduce the notion of a functor having a presen
 tation by operations and equations. The functors having a finitary such pr
 esentation are characterized as the functors that preserve sifted colimits
 . b) The classic theorems of Jonsson-Tarski and Goldblatt-Thomason in Moda
 l Logic become theorems on algebras over the Ind- and Pro-completions of a
  category.\n\n[The results are from joint work with M. Bonsangue and with 
 J. Rosicky]
LOCATION:Room FW11\, Computer Laboratory\, William Gates Building
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