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International Conference on Automated Deduction

CADE 2019: Automated Deduction – CADE 27 pp 142–160Cite as

Model Completeness, Covers and Superposition

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 11716))

Abstract

In ESOP 2008, Gulwani and Musuvathi introduced a notion of cover and exploited it to handle infinite-state model checking problems. Motivated by applications to the verification of data-aware processes, we show how covers are strictly related to model completions, a well-known topic in model theory. We also investigate the computation of covers within the Superposition Calculus, by adopting a constrained version of the calculus, equipped with appropriate settings and reduction strategies.

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Notes

  1. 1.

    Partial correctness means that, when the algorithm terminates, it gives a correct answer. Effectiveness means that all subprocedures in the algorithm can be effectively executed.

  2. 2.

    We say that T is locally finite iff for every finite tuple of variables \(\underline{x}\) there are only finitely many non T-equivalent atoms \(A(\underline{x})\) involving only the variables \(\underline{x}\).

  3. 3.

    One may restrict to models interpreting sorts as finite sets, as customary in database theory. Since the theories we are dealing with usually have finite model property for constraint satisfiability, assuming such restriction turns out to be irrelevant, as far as safety problems are concerned (see [11, 12] for an accurate discussion).

  4. 4.

    This example points out a problem that needs to be fixed in the algorithm presented in [25]: that algorithm in fact outputs only equalities, conditional equalities and single disequalities, so it cannot correctly handle this example.

  5. 5.

    Notice that, in the above definition of degree, constraints (attached to the rewriting rules occurring in our calculus) are ignored.

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Acknowledgements

This research has been partially supported by the UNIBZ CRC projects REKAP: Reasoning and Enactment for Knowledge-Aware Processes and PWORM: Planning for Workflow Management.

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Authors and Affiliations

  1. Faculty of Computer Science, Free University of Bozen-Bolzano, Bolzano, Italy

    Diego Calvanese, Alessandro Gianola, Marco Montali & Andrey Rivkin

  2. Dipartimento di Matematica, Università degli Studi di Milano, Milan, Italy

    Silvio Ghilardi

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  1. Diego Calvanese
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  2. Silvio Ghilardi
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Correspondence to Alessandro Gianola .

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  1. University of Lorraine, Villers-lès-Nancy, France

    Pascal Fontaine

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Calvanese, D., Ghilardi, S., Gianola, A., Montali, M., Rivkin, A. (2019). Model Completeness, Covers and Superposition. In: Fontaine, P. (eds) Automated Deduction – CADE 27. CADE 2019. Lecture Notes in Computer Science(), vol 11716. Springer, Cham. https://doi.org/10.1007/978-3-030-29436-6_9

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