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Articles 61 - 66 of 66
Full-Text Articles in Logic and Foundations
Preface, Alexander Kurz
Preface, Alexander Kurz
Engineering Faculty Articles and Research
No abstract provided.
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.
Modal Rules Are Co-Implications, Alexander Kurz
Modal Rules Are Co-Implications, Alexander Kurz
Engineering Faculty Articles and Research
In [13], it was shown that modal logic for coalgebras dualises—concerning definability— equational logic for algebras. This paper establishes that, similarly, modal rules dualise implications:It is shown that a class of coalgebras is definable by modal rules iff it is closed under H (images) and Σ (disjoint unions). As a corollary the expressive power of rules of infinitary modal logic on Kripke frames is characterised.
Notes On Coalgebras, Cofibrations And Concurrency, Alexander Kurz, Dirk Pattinson
Notes On Coalgebras, Cofibrations And Concurrency, Alexander Kurz, Dirk Pattinson
Engineering Faculty Articles and Research
We consider categories of coalgebras as (co)-fibred over a base category of parameters and analyse categorical constructions in the total category of deterministic and non-deterministic coalgebras.
(Ω, Ξ)-Logic: On The Algebraic Extension Of Coalgebraic Specifications, Rolf Hennicker, Alexander Kurz
(Ω, Ξ)-Logic: On The Algebraic Extension Of Coalgebraic Specifications, Rolf Hennicker, Alexander Kurz
Engineering Faculty Articles and Research
We present an extension of standard coalgebraic specification techniques for statebased systems which allows us to integrate constants and n-ary operations in a smooth way and, moreover, leads to a simplification of the coalgebraic structure of the models of a specification. The framework of (Ω,Ξ)-logic can be considered as the result of a translation of concepts of observational logic (cf. [9]) into the coalgebraic world. As a particular outcome we obtain the notion of an (Ω, Ξ)- structure and a sound and complete proof system for (first-order) observational properties of specifications.