Results 1 
5 of
5
Semantical Principles in the Modal Logic of Coalgebraic
"... Coalgebras for a functor on the category of sets subsume many formulations of the notion of transition system, including labelled transition systems, Kripke models, Kripke frames and many types of automata. This paper presents a multimodal language which is bisimulation invariant and (under a natur ..."
Abstract

Cited by 30 (6 self)
 Add to MetaCart
Coalgebras for a functor on the category of sets subsume many formulations of the notion of transition system, including labelled transition systems, Kripke models, Kripke frames and many types of automata. This paper presents a multimodal language which is bisimulation invariant and (under a natural completeness condition) expressive enough to characterise elements of the underlying state space up to bisimulation. Like Moss' coalgebraic logic, the theory can be applied to an arbitrary signature functor on the category of sets. Also, an upper bound for the size of conjunctions and disjunctions needed to obtain characteristic formulas is given.
Coalgebraic Modal Logic of Finite Rank
, 2002
"... This paper studies coalgebras from the perspective of finite observations. We introduce the notion of finite step equivalence and a corresponding category with finite step equivalencepreserving morphisms. This category always has a final object, which generalises the canonical model construction fr ..."
Abstract

Cited by 14 (8 self)
 Add to MetaCart
This paper studies coalgebras from the perspective of finite observations. We introduce the notion of finite step equivalence and a corresponding category with finite step equivalencepreserving morphisms. This category always has a final object, which generalises the canonical model construction from Kripke models to coalgebras. We then turn to logics whose formulae are invariant under finite step equivalence, which we call logics of rank . For these logics, we use topological methods and give a characterisation of compact logics and definable classes of models.
Definability, Canonical Models, Compactness for Finitary Coalgebraic Modal Logic
, 2007
"... 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 ..."
Abstract

Cited by 5 (3 self)
 Add to MetaCart
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.
Final Coalgebras
"... That is, makes the diagram C R 1 oo 2 // D TC TR T1 oo T2 // TD 1 commute. We call a pair (c; d) 2 C D bisimilar, if 9R C D. R bisimulation and (c; d) 2 R. If c and d are bisimilar, this is denoted by c  d. 2 On Bisimulation If f : A ! B is a function, denote its Graph b ..."
Abstract
 Add to MetaCart
That is, makes the diagram C R 1 oo 2 // D TC TR T1 oo T2 // TD 1 commute. We call a pair (c; d) 2 C D bisimilar, if 9R C D. R bisimulation and (c; d) 2 R. If c and d are bisimilar, this is denoted by c  d. 2 On Bisimulation If f : A ! B is a function, denote its Graph by G(f) = f(a; f(a)) j a 2<F12.2