Modal Logics for Coalgebras
نویسنده
چکیده
This presentation is to introduce basic notions and recent results on an approach to specify behaviors of coalgebras by means of modal logics, based on the lecture by Dirk Pattinson (Pattinson, 2003) in NASSLLI 2003.
منابع مشابه
Ultrafilter Extensions for Coalgebras
This paper studies finitary modal logics as specification languages for Set-coalgebras (coalgebras on the category of sets) using Stone duality. It is wellknown that Set-coalgebras are not semantically adequate for finitary modal logics in the sense that bisimilarity does not in general coincide with logical equivalence. Stone-coalgebras (coalgebras over the category of Stone spaces), on the ot...
متن کاملCoalgebraic semantics of modal logics: An overview
Coalgebras can be seen as a natural abstraction of Kripke frames. In the same sense, coalgebraic logics are generalised modal logics. In this paper, we give an overview of the basic tools, techniques and results that connect coalgebras and modal logic. We argue that coalgebras unify the semantics of a large range of different modal logics (such as probabilistic, graded, relational, conditional)...
متن کاملModal Logics for Observation Equivalences
In our paper [RM02a] we describe an approach to weak bisimulation for coalgebras and show that parts of the theory of universal coalgebra (with strong bisimulation) can be obtained when considering coalgebras with weak bisimulations and weak homomorphisms. In the present paper we focus on uniformly adapting modal logics that characterise strong bisimulation for coalgebras to several kinds of ob...
متن کاملUniversal Coalgebras and Their Logics
We survey coalgebras as models of state based systems together with their global and local logics. We convey some useful intuition regarding Set-functors which leads naturally to coalgebraic modal logic where modalities are validity patterns for the successor object of a state.
متن کاملRank-1 Modal Logics Are Coalgebraic
Coalgebras provide a unifying semantic framework for a wide variety of modal logics. It has previously been shown that the class of coalgebras for an endofunctor can always be axiomatised in rank 1. Here we establish the converse, i.e. every rank 1 modal logic has a sound and strongly complete coalgebraic semantics. As a consequence, recent results on coalgebraic modal logic, in particular gene...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2003