Alexander Kurz and Nick Bezhanishvili are organising a workshop on topics loosely related to coalgebras, and category and domain theory this week, 28 and 29 May 2009. Originally planned to be between the Imperial College, London and the University of Leicester, we expect guests from Birmingham, Cambridge, and Southampton. Alexander asked me to present our work on trace logics. If you are interested, do join and find the title and abstract below. A concise schedule seems not to be available; the workshop will begin on Thursday at 11am and end on Friday at 4:30pm.

 Title: Trace Logics for Semiring Monads

 Abstract:  Recently, coalgebraic logics have seen much attention as means to characterise points in Set-based coalgebras precisely up to bisimilarity. With the introduction of a uniform definition of trace semantics for coalgebras structured in the branching type given by a monad, the question was raised for a logic which describes points in such coalgebras adequately and expressively up to trace equivalence.

 In this talk I will present recent work with Alexander Kurz on this question. We consider coalgebras on Set with branching given by evaluation in a fixed semiring, which defines a semiring monad. The trace semantics of such coalgebras is given by final sequence induction in the Kleisli-category, which in this case happens to be the category of freely generated semimodules. We then obtain trace logics and its semantics as transposes of respectively final coalgebra and final coalgebra morphism along the Morita adjunction induced by the semiring under consideration.