Title: Towards a Coalgebraic Interpretation of Propositional Dynamic Logic

Speaker: Ernst-Erich Doberkat, Chair for Software Technology,

Technische Universit ̈at Dortmund, Germany

Time: 3:00pm, July 27th(Wednesday), 2011.

Venue: Lecture Room, 3rd Floor, Building No. 5, State Key Laboratory of Computer Science, Institute of Software, Chinese Academy of Sciences

Abstract:

The interpretation of propositional dynamic logic (PDL) through Kripke models requires the relations constituting the interpreting Kripke model to closely observe the syntax of the modal operators. This poses a significant challenge for an interpretation of PDL through stochastic Kripke models, because the  programs’ operations do not always have a natural counterpart in the set of stochastic relations. We use rewrite rules for building up an interpretation of PDL. It is shown that each program corresponds to an essentially unique irreducible tree, which in turn is assigned a predicate lifting, serving as the program’s interpretation. This interpretation is established and studied. We discuss the expressivity of probabilistic models for PDL and — if there is time — relate properties like logical and behavioral equivalence or bisimilarity to the corresponding properties of a Kripke model for a closely related non-dynamic logic of the Hennessy-Milner type.

Biography:

Education: Dipl.-Math. from the University of Bochum with a minor in Philosophy, Dr. rer. nat. in Mathematics from the University of Paderborn, Dr. rer. nat. habil. in Computer Science from the University of Hagen.

Positions: Associate Professor of Mathematics and Computer Science, Clarkson College of Technology, Potsdam, NY; Full Professor of Practical Computer Science, University of Hildesheim, Full Professor of Software Engineering, University of Essen (Chairman of the Department of Mathematics); since 1993 Full Professor and Chair of Software Technology at the Technical University of Dortmund, currently also Adjunct Professor of Mathematics.

Research Interests: Specification languages, software reuse, requirements engineering for computer applications in the humanities, computer science education and multimedia, algebras and coalgebras for probabilistic monads, stochastic Kripke models for modal and coalgebraic logics, universal algebra, stochastic relations.