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From Model Completeness to Verification of Data Aware Processes

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Book cover Description Logic, Theory Combination, and All That

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11560))

Abstract

Model Completeness is a classical topic in model-theoretic algebra, and its inspiration sources are areas like algebraic geometry and field theory. Yet, recently, there have been remarkable applications in computer science: these applications range from combined decision procedures for satisfiability and interpolation, to connections between temporal logic and monadic second order logic and to model-checking. In this paper we mostly concentrate on the last one: we study verification over a general model of so-called artifact-centric systems, which are used to capture business processes by giving equal important to the control-flow and data-related aspects. In particular, we are interested in assessing (parameterized) safety properties irrespectively of the initial database instance. We view such artifact systems as array-based systems, establishing a correspondence with model checking based on Satisfiability-Modulo-Theories (SMT). Model completeness comes into the picture in this framework by supplying quantifier elimination algorithms for suitable existentially closed structures. Such algorithms, whose complexity is unexpectedly low in some cases of our interest, are exploited during search and to represent the sets of reachable states. Our first implementation, built up on top of the mcmt model-checker, makes all our foundational results fully operational and quite effective, as demonstrated by our first experiments.

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Notes

  1. 1.

    http://smtlib.cs.uiowa.edu/.

  2. 2.

    It is quite curious to notice that this observation (in its essence) was already present in the paper [45], where however model completeness was not mentioned at all! Instead of quantifier elimination in the model completion \(T^*\), the authors of [45] relied on the computation of the so called ‘cover’ of an existential formula (such cover turns out to be equivalent to the quantifier free equivalent formula modulo \(T^*\)).

  3. 3.

    Again, without mentioning any specific application, this was already observed in [45], as the specialization of the cover algorithm to signatures with unary free function symbols.

  4. 4.

    For the purposes of this definition, we may equivalently take the formula to be quantifier-free.

  5. 5.

    Arity and source/target sorts for F can be deduced from the context (considering that everything is well-typed).

  6. 6.

    This directly implies that \(\phi \) is satisfiable also in a DB instance that interprets value sorts into finite sets.

  7. 7.

    By ‘signature’ we always mean ‘signature with equality’, so as soon as new sorts are added, the corresponding equality predicates are added too.

  8. 8.

    In accordance with mcmt conventions, we denote the application of an artifact component a to a term (i.e., constant or variable) v also as a[v] (standard notation for arrays), instead of a(v).

  9. 9.

    Recall that \(a_j =\lambda y. d_{j}\) abbreviates \(\forall y\, a_{j}(y)=d_{j}\).

  10. 10.

    Non-deterministic updates can be formalized using existentially quantified variables in the transition.

  11. 11.

    This is unrelated to cyclicity of \(\varSigma \) defined in Sect. 3, and comes from universal algebra terminology.

  12. 12.

    http://users.mat.unimi.it/users/ghilardi/mcmt/, subdirectory /examples/dbdriven of the distribution. The user manual contains a new section (pages 36–39) on how to encode RAS s in MCMT specifications.

  13. 13.

    http://www.bpmn.org/.

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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

Authors
  1. Diego Calvanese
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  2. Silvio Ghilardi
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  3. Alessandro Gianola
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  4. Marco Montali
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  5. Andrey Rivkin
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Correspondence to Alessandro Gianola .

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Editors and Affiliations

  1. University of Bremen, Bremen, Germany

    Carsten Lutz

  2. University of Manchester, Manchester, UK

    Uli Sattler

  3. University of Iowa, Iowa City, IA, USA

    Cesare Tinelli

  4. TU Dresden, Dresden, Germany

    Anni-Yasmin Turhan

  5. University of Liverpool, Liverpool, UK

    Frank Wolter

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Calvanese, D., Ghilardi, S., Gianola, A., Montali, M., Rivkin, A. (2019). From Model Completeness to Verification of Data Aware Processes. In: Lutz, C., Sattler, U., Tinelli, C., Turhan, AY., Wolter, F. (eds) Description Logic, Theory Combination, and All That. Lecture Notes in Computer Science(), vol 11560. Springer, Cham. https://doi.org/10.1007/978-3-030-22102-7_10

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