International Workshop: Coalgebraic Logic

The coalgebraic approach to logics is an active and young research field. It has been driven mainly by two insights. First, thatcoalgebras serve as a uniform model of systems. Second, that a similarly uniform account of logics for transition systems would be highly desirable for practitioners in Computer Science; specifically those who work on the specification and verification of properties of distributed and mobile systems.Recently, it appeared that the mathematical theory of dualityoriginating in Stone duality forBoolean algebras might be the right tool to achieve such a uniform account of logics fortransition systems. Preliminary work by one of the proposers, Alexander Kurz, and colleagues yielded tight connections of coalgebraic logic withresearch done by the other two proposers (Hilary Priestley and MaiGehrke) and others. This revealed, in particular, the relevance of canonical extensions and Sahlqvist formula to coalgebraic logic. These insights led to a joint EPSRC-funded project (Jan-July 2007) on which Gehrke is visiting fellow.The present state of the art in the theory of coalgebras is such thatthe time is ripe for a focused workshop, aimed at identifying keymathematical needs in coalgebraic logic and its computer science applications. Oxford University is to host the internationalconference ALGEBRAIC AND TOPOLOGICAL METHODS IN NON-CLASSICAL LOGICSIII' (TANCL'07) in August 2007; at the first two conferences in theseries, in Tbilisi, Republic of Georgia (2003) and in Barcelona (2005)informal discussions took place which opened up connections betweenthe research interests of the `TANCL community' and those of coalgebraspecialists. The TANCL conference in Oxford provides a unique, and unmissable, opportunity to hold a workshop meeting in the UK oncoalgebraic logic. This will bring together coalgebraists from the UKand beyond and international researchers in cognate areas of mathematics, to pursue and to deepen the connections between their fields. The interdisciplinary aspect of the Workshop is a cruciallyimportant feature.The programme of the workshop is structured according to threetopics. The main thrust of Topic 1 is to connect what themathematicians have to offer and what thecoalgebra-in-computer-science community can use, both conceptually andtechnically. Topics 2 and 3 address two issues at the frontiersof current knowledge. Both represent directions of research that must be urgently pursued in order that coalgebraic logic be developed to the point where it fulfills its potential to be of real practical value in thespecification and verification of distributed andmobile systems.