Bialgebras and modal logic

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• Bartek Klin, University of Edinburgh
• Friday 10 November 2006, 14:00-15:00
• FW11.

If you have a question about this talk, please contact Tom Ridge.

Bialgebraic semantics is a categorical approach to modelling well-behaved structural operational semantics (SOS), parametrised by notions of syntax and behaviour. Invented by Turi and Plotkin a decade ago, it allows us to derive formats for SOS descriptions of various “kinds” of systems (including labelled transition systems, probabilistic or timed systems etc.) in a systematic way. In each case, the canonical process equivalence related to the “kind”, or behaviour of systems, is guaranteed compositional. The well-known GSOS format can be seen as a special case of the bialgebraic approach, where the behaviour is the one for labelled transition systems and bisimilarity is compositional.

The original bialgebraic setting deals only with a single, canonical equivalence for each behaviour. In this talk I will show how to make the setting more flexible to accommodate other equivalences, e.g., trace or completed trace equivalences for labelled transition systems. To this end, I will show how to combine bialgebraic techniques with the coalgebraic approach to modal logic, to obtain “logical duals” to structural operational semantic descriptions.

This talk is part of the Logic and Semantics Seminar (Computer Laboratory) series.

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