Equational axiomatizability for coalgebra

Equational Axiomatizability for Coalgebra

A characterization result for equationally de nable classes of certain coalgebras (including basic hidden algebra) shows that a class of coalgebras is de nable by equations if and only if it is closed under coproducts, quotients, sources of morphisms and representative inclusions. The notions of equation and satisfaction are axiomatized in order to include the di erent approaches in the literat...

Axiomatizability in Inclusive Equational Logic

On the Axiomatizability of Ready Traces, Ready Simulation, and Failure Traces

We provide an answer to an open question, posed by van Glabbeek [4], regarding the axiomatizability of ready trace semantics. We prove that if the alphabet of actions is finite, then there exists a (sound and complete) finite equational axiomatization for the process algebra BCCSP modulo ready trace semantics. We prove that if the alphabet is infinite, then such an axiomatization does not exist...

A Birkhoo-like Axiomatizability Result for Hidden Algebra and Coalgebra

A characterization result for behaviorally deenable classes of hidden algebras shows that a class of hidden algebras is behaviorally deenable by equations if and only if it is closed under coproducts, quotients, morphisms and representative inclusions. The second part of the paper categorically generalizes this result to a framework of any category with coproducts, a nal object and an inclusion...

Cylindric algebras and relational databases

An interpretation of the relational data model and various dependencies is given within the framework of cylindric algebras. It turns out that there is a natural translation of relational databases into cylindric set lattices, and that Codd’s relational operators have a simple interpretation in these structures. Consequently, various database constraints can be expressed in the equational langu...