We show that certain fixpoint expressions used to describe finite Kripke polynomial coalgebras can be seen as coalgebraic modal fixpoint formulae. Both the synthesis of a coalgebra from its expression and the ability to check behavioural equivalence follow from the same tableau construction. There is an associated complete equational logic, analogous to Kleene algebra, which may now be seen as ...

We use the connection between automata and logic to prove that a wide class of coalgebraic fixpoint logics enjoys uniform interpolation. To this aim, first we generalize one of the central results in coalgebraic automata theory, namely closure under projection, which is known to hold for weak-pullback preserving functors, to a more general class of functors, i.e.; functors with quasi-functorial...

A constructively valid counterpart to Bourbaki’s Fixpoint Lemma for chaincomplete partially ordered sets is presented to obtain a condition for one closure system in a complete lattice L to be stable under another closure operator of L. This is then used to deal with coproducts and other aspects of frames.

ion in Fixpoint Logic SJOERD CRANEN, MACIEJ GAZDA, WIEGER WESSELINK and TIM A.C. WILLEMSE, Eindhoven University of Technology We present a theory of abstraction for the framework of parameterised Boolean equation systems, a firstorder fixpoint logic. Parameterised Boolean equation systems can be used to solve a variety of problems in verification. We study the capabilities of the abstraction th...

The finite satisfiability problem for guarded fixpoint logic is decidable and complete for 2ExpTime (resp. ExpTime for formulas of bounded width).

Fixpoint Computations with Numerical Acceleration Methods Olivier Bouissou and Yassamine Seladji CEA, LIST, Laboratory for the Modeling and Analysis of Interacting Systems 91191 Gif-sur-Yvette, France

We present the concept of a disjunctive basis as a generic framework for normal forms in modal logic based on coalgebra. Disjunctive bases were defined in previous work on completeness for modal fixpoint logics, where they played a central role in the proof of a generic completeness theorem for coalgebraic mu-calculi. Believing the concept has a much wider significance, here we investigate it m...