Verifying that a temporal logic specification satisfies a temporal property requires some form of theorem proving. However, although proof procedures exist for such logics, many are either unsuitable for automatic implementation or only deal with small fragments of the logic. In this thesis the algorithms for, and strategies to guide, a fully automated temporal resolution theorem prover are given, proved correct and evaluated. An approach to applying resolution, a proof method for classical logics suited to mechanisation, to temporal logics has been developed by Fisher. The method involves translation to a normal form, classical style resolution within states and temporal resolution over states. It has only one temporal resolution rule and is therefore particularly suitable as the basis of an automated temporal resolution theorem prover. As the application of the temporal resolution rule is the most costly part of the method, involving search amongst graphs, different algorithms on w...

. In this paper we give and evaluate the algorithms for a fully automated temporal resolution theorem prover. An approach to applying resolution, a proof method for classical logics suited to mechanisation, to temporal logics has been developed by Fisher. As the application of the temporal resolution rule is the most costly part of the method, involving search amongst graphs, we propose different algorithms on which to base an implementation. The paper concludes with a comparison of their performance. 1 Introduction Temporal logics have been used extensively for the specification and verification of properties of concurrent systems, see for example [Hai82, Lam83, MP92]. However proof procedures for such logics have tended to be tableau [Wol85, Gou84] or automata [VW86] based rather than based on resolution [Rob65]. In many cases the resolution based decision procedures that have been developed for temporal logics [CdC84, Ven86, AM90] are unsuitable for implementation because they only...

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Graph transformation techniques have already been used successfully by several research groups to support re-engineering of large legacy systems. Where others often aim at transforming the system to improve it, we advocate an evolutionary approach that embeds transformations within the ordinary development process and provides tool support to monitor the ongoing progress regularly. In this paper, we discuss how temporal graph queries based on Fujaba story diagrams can provide a natural means to express trend-oriented metrics and consistency rules that we identified in our industrial case studies. To this end, we discuss a first-order logic rather than operational interpretation of a graph queries and show how well-known temporal logic operators can be added to express rules over consecutive states of the same instance graph.

This report is an extended version of an article published elsewhere. This paper introduces a new decision procedure for PLTL based on labelled superposition. Its main idea is to treat temporal formulas as infinite sets of purely propositional clauses over an extended signature. These infinite sets are then represented by finite sets of labelled propositional clauses. The new representation enables the replacement of the complex temporal resolution rule, suggested by existing resolution calculi for PLTL, by a fine grained repetition check of finitely saturated labelled clause sets followed by a sim-ple inference. The completeness argument is based on the standard model building idea from superposition. It inherently justifies ordering restrictions, redundancy elimination and effective partial model building. The latter can be directly used to effectively generate counterexamples of non-valid PLTL conjectures out of saturated labelled clause sets in a straightforward way.