Sebastian Enqvist: Disjunctive bases: a coalgebraic approach to normal forms in modal logic
Tid: On 2019-02-20 kl 10.00 - 11.45
Föreläsare: Sebastian Enqvist (Stockholm University)
Plats: Room 16, building 5, Kräftriket, Department of Mathematics, Stockholm University
Abstract: I present the concept of a disjunctive basis, a generic framework for normal forms in modal logic based on coalgebra, and provide some illustrating examples. The presence of a disjunctive basis entails a number of good properties for a coalgebraic modal logic and its mu-calculus extension, in particular, a simulation theorem showing that every alternating automaton can be transformed into an equivalent nondeterministic one. This leads to a number of results: a Lyndon theorem for the full fixpoint logic, its fixpoint-free fragment and its one-step fragment, a Uniform Interpolation result, for both the full mu-calculus and its fixpoint-free fragment, and a Janin-Walukiewicz-style characterization theorem for the mu-calculus under slightly stronger assumptions. Furthermore, existence of a disjunctive basis is closed under some natural operations for modular construction of coalgebraic logics: sum, product and composition.
The talk is based on joint work with Yde Venema.