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Erschienen in:
2014 | OriginalPaper | Buchkapitel
A Coalgebraic Approach to Linear-Time Logics
verfasst von : Corina Cîrstea
Erschienen in: Foundations of Software Science and Computation Structures
Verlag: Springer Berlin Heidelberg
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We extend recent work on defining linear-time behaviour for state-based systems with branching, and propose modal and fixpoint logics for specifying linear-time temporal properties of states in such systems. We model systems with branching as coalgebras whose type arises as the composition of a branching monad and a polynomial endofunctor on the category of sets, and employ a set of truth values induced canonically by the branching monad. This yields logics for reasoning about quantitative aspects of linear-time behaviour. Examples include reasoning about the probability of a linear-time behaviour being exhibited by a system with probabilistic branching, or about the minimal cost of a linear-time behaviour being exhibited by a system with weighted branching. In the case of non-deterministic branching, our logic supports reasoning about the
possibility
of exhibiting a given linear-time behaviour, and therefore resembles an existential version of the logic LTL.