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Adequate Sets of Temporal Connectives in CTL

✍ Scribed by Alan Martin

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
252 KB
Volume
52
Category
Article
ISSN
1571-0661

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✦ Synopsis

An adequate set of temporal connectives for CTL is a subset of the logic's temporal connectives that is sufficient to express equivalents for all CTL formulas.

In this paper, a characterization of all such adequate sets is presented. Specifically, it is shown that a subset of CTL's temporal connectives is adequate if and only if it contains one of ({\mathrm{AX}, \mathrm{EX}}), one of ({\mathrm{EG}, \mathrm{AF}, \mathrm{AU}}), and (\mathrm{EU}).

The proof requires, among other things, the analysis of a certain class of models, the reflexive models. These models have the desirable property that several connectives become redundant, thus simplifying the analysis.

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