منابع مشابه
Rank-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 کاملModal Logics are Coalgebraic
Applications of modal logics are abundant in computer science, and a large number of structurally different modal logics have been successfully employed in a diverse spectrum of application contexts. Coalgebraic semantics, on the other hand, provides a uniform and encompassing view on the large variety of specific logics used in particular domains. The coalgebraic approach is generic and compos...
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 کاملInternal Models for Coalgebraic Modal Logics
We present ongoing work into the systematic study of the use of dual adjunctions in coalgebraic modal logic. We introduce a category of internal models for a modal logic. These are constructed from syntax, and yield a generalised notion of canonical model. Further, expressivity of a modal logic is shown to be characterised by factorisation of its models via internal models and the existence of ...
متن کاملSimulations and Bisimulations for Coalgebraic Modal Logics
Simulations serve as a proof tool to compare the behaviour of reactive systems. We define a notion of Λ-simulation for coalgebraic modal logics, parametric in the choice of a set Λ of monotone predicate liftings for a functor T . That is, we obtain a generic notion of simulation that can be flexibly instantiated to a large variety of systems and logics, in particular in settings that semantical...
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ژورنال
عنوان ژورنال: Journal of Logic and Computation
سال: 2008
ISSN: 0955-792X,1465-363X
DOI: 10.1093/logcom/exn096