Elsevier

Theoretical Computer Science

Volume 412, Issue 38, 2 September 2011, Pages 5025-5042
Theoretical Computer Science

Maximal traces and path-based coalgebraic temporal logics

https://doi.org/10.1016/j.tcs.2011.04.025Get rights and content
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Abstract

This paper gives a general coalgebraic account of temporal logics whose semantics involves a notion of computation path. Examples of such logics include the logic CTL* for transition systems and the logic PCTL for probabilistic transition systems. Our path-based temporal logics are interpreted over coalgebras of endofunctors obtained as the composition of a computation type (e.g. non-deterministic or stochastic) with a general transition type. The semantics of such logics relies on the existence of execution maps similar to the trace maps introduced by Jacobs and co-authors as part of the coalgebraic theory of finite traces (Hasuo et al., 2007 [1]). We consider finite execution maps derived from the theory of finite traces, and a new notion of maximal execution map that accounts for maximal, possibly infinite executions. The latter is needed to recover the logics CTL* and PCTL as specific path-based logics.

Keywords

Coalgebra
Trace semantics
Computation path
Temporal logic
Non-determinism
Probability

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