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Other Computer Engineering Commons

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Chapman University

Other Mathematics

2002

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 Jan 2002

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 Jan 2002

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 Jan 2002

Preface, Alexander Kurz

Engineering Faculty Articles and Research

No abstract provided.