Coalgebra and Logic: A Brief Overview

Several researchers have collaborated to publish an overview of coalgebra and logic in the special issue of the Journal of Logic and Computation. They have informed that the idea of coalgebra is general enough to encompass structures that are not usually perceived as relational structures or transition systems. A coalgebra ξ resembles a topological space for TX=(PX)(2x) and helps in obtaining Chellas's conditional frames. Two states are defined in such a coalgebra to be behaviorally equivalent when they can be identified by some coalgebra morphism. This means in the case of deterministic automata that the two states induce the same accepted language. It is also observed that satisfiability of coalgebraic logic can be established in PSPACE and that complete coalgebraic logics have the finite model property.