Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 3 of 3
Full-Text Articles in Other Computer Engineering
Definability, Canonical Models, And Compactness For Finitary Coalgebraic Modal Logic, Alexander Kurz, Dirk Pattinson
Definability, Canonical Models, And Compactness For Finitary Coalgebraic Modal Logic, Alexander Kurz, Dirk Pattinson
Engineering Faculty Articles and Research
This paper studies coalgebras from the perspective of the finitary observations that can be made of their behaviours. Based on the terminal sequence, notions of finitary behaviours and finitary predicates are introduced. A category Behω(T) of coalgebras with morphisms preserving finitary behaviours is defined. We then investigate definability and compactness for finitary coalgebraic modal logic, show that the final object in Behω(T) generalises the notion of a canonical model in modal logic, and study the topology induced on a coalgebra by the finitary part of the terminal sequence.
Modal Predicates And Coequations, Alexander Kurz, Jiří Rosický
Modal Predicates And Coequations, Alexander Kurz, Jiří Rosický
Engineering Faculty Articles and Research
We show how coalgebras can be presented by operations and equations. This is a special case of Linton’s approach to algebras over a general base category X, namely where X is taken as the dual of sets. Since the resulting equations generalise coalgebraic coequations to situations without cofree coalgebras, we call them coequations. We prove a general co-Birkhoff theorem describing covarieties of coalgebras by means of coequations. We argue that the resulting coequational logic generalises modal logic.
Preface, Alexander Kurz
Preface, Alexander Kurz
Engineering Faculty Articles and Research
No abstract provided.