Equational Logic of Polynomial Coalgebras

Coalgebraic Expressions

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 ...

Equational Logi of Polynomial Coalgebras

Some Sahlqvist Completeness Results for Coalgebraic Logics

This paper presents a first step towards completeness-viacanonicity results for coalgebraic modal logics. Specifically, we consider the relationship between classes of coalgebras for ω-accessible endofunctors and logics defined by Sahlqvist-like frame conditions. Our strategy is based on conjoining two well-known approaches: we represent accessible functors as (equational) quotients of polynomi...

Research of Alexander Kurz

Coalgebras When I started my PhD, the idea that the theory of coalgebras might serve as a general theory of systems had emerged. But there were only a few ad hoc descriptions of speci cation languages for coalgebras which were built, in analogy with logics for algebras, on equational logic and extensions. [2] was one of the rst papers to put forward the idea that modal logics should be used as ...

A Complete Calculus for Equational Deduction in Coalgebraic Specification A. Corradini a Complete Calculus for Equational Deduction in Coalgebraic Speciication

The use of coalgebras for the speciication of dynamical systems with a hidden state space is receiving more and more attention in the years, as a valid alternative to algebraic methods based on observational equivalences. However, to our knowledge, the coalgebraic framework is still lacking a complete equational deduction calculus which enjoys properties similar to those stated in Birkhoo's com...