Abstract
Recently, local logics for Mazurkiewicz traces are of increasing interest. This is mainly due to the fact that the satisfiability problem has the same complexity as in the word case. If we focus on a purely local interpretation of formulae at vertices (or events) of a trace, then the satisfiability problem of linear temporal logics over traces turns out to be PSPACE-complete. But now the dificult problem is to obtain expressive completeness results with respect to first order logic. The main result of the paper shows such an expressive completeness result, if the underlying dependence alphabet is a cograph, i.e., if all traces are series parallel graphs. Moreover, we show that this is the best we can expect in our setting: If the dependence alphabet is not a cograph, then we cannot express all first order properties.
Partial support of EC-FET project IST-1999-29082 (ADVANCE), CEFIPRAIFCPAR Project 2102-1 (ACSMV) and PROCOPE project 00269SD (MoVe) is gratefully acknowledged.
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Diekert, V., Gastin, P. (2001). Local Temporal Logic Is Expressively Complete for Cograph Dependence Alphabets. In: Nieuwenhuis, R., Voronkov, A. (eds) Logic for Programming, Artificial Intelligence, and Reasoning. LPAR 2001. Lecture Notes in Computer Science(), vol 2250. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45653-8_4
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