research-article

Paraconsistent reasoning for inconsistency measurement in declarative process specifications

Authors:

Isabelle Kuhlmann,

Matthias Thimm,

John GrantAuthors Info & Claims

Volume 122, Issue C

https://doi.org/10.1016/j.is.2024.102347

Published: 01 May 2024 Publication History

Abstract

Inconsistency is a core problem in fields such as AI and data-intensive systems. In this work, we address the problem of measuring inconsistency in declarative process specifications, with an emphasis on linear temporal logic (LTL). As we will show, existing inconsistency measures for classical logic cannot provide a meaningful assessment of inconsistency in LTL in general, as they cannot adequately handle the temporal operators. We therefore propose a novel paraconsistent semantics for LTL over fixed traces (LTLff) as a framework for time-sensitive inconsistency measurement. We develop and implement novel approaches for (element-based) inconsistency measurement, and propose a novel semantics for reasoning in LTLff in the presence of preference relations between formulas. We implement our approach for inconsistency measurement with Answer Set Programming and evaluate our results with real-life data sets from the Business Process Intelligence Challenge.

Highlights

•

We present an approach for measuring inconsistency in declarative process specifications.

•

We use Linear Temporal Logic on fixed traces (LTLff) and a paraconsistent semantics.

•

We develop a series of “time-sensitive” inconsistency measures, also for pin-pointing issues.

•

We extend the framework with a preference relation over LTLff constraints.

•

We develop and show-case algorithmic approaches for our approach.

References

[1]

Pnueli A., The temporal logic of programs, in: 18th Symposium on Foundations of Computer Science, Rhode Island, IEEE Computer Society, 1977, pp. 46–57.

[2]

Cecconi A., De Giacomo G., Di Ciccio C., Maggi F.M., Mendling J., A temporal logic-based measurement framework for process mining, in: Proceedings of the 2nd ICPM, IEEE, 2020, pp. 113–120.

[3]

Di Ciccio C., Maggi F.M., Montali M., Mendling J., Resolving inconsistencies and redundancies in declarative process models, Inf. Syst. 64 (2017) 425–446.

Digital Library

[4]

Corea C., Nagel S., Mendling J., Delfmann P., Interactive and minimal repair of declarative process models, in: BPM Forum, Rome, Springer, 2021, pp. 3–19.

[5]

Roveri M., Di Ciccio C., Di Francescomarino C., Ghidini C., Computing unsatisfiable cores for LTLf specifications, 2022, (Preprint) arXiv.

[6]

Grant J., Martinez M.V., Measuring Inc. in Information, College Pub., 2018.

[7]

Thimm M., Inconsistency measurement, in: Proceedings of the 13th International Conference on Scalable Uncertainty Management, Compiègne, Springer, 2019.

[8]

Corea C., Grant J., Thimm M., Measuring inconsistency in declarative process specifications, in: Proceedings of the 20th International Conference on Business Process Management, in: Lecture Notes in Computer Science, vol. 13420, BPM 2022, Münster, Germany, Springer, 2022, pp. 289–306.

[9]

Hunter A., Konieczny S., et al., Shapley inconsistency values, KR 6 (2006) 249–259.

[10]

Thimm M., Wallner J.P., On the complexity of inc. meas, AI 275 (2019) 411–456.

[11]

Grant J., Hunter A., Measuring consistency gain and inf. loss in stepwise inc. resolution, in: Proc. of the 11th ECSQARU, Belfast, Springer, 2011, pp. 362–373.

[12]

Priest G., Logic of paradox, J. Philos. Logic 8 (1979) 219–241.

[13]

Hunter A., Konieczny S., Measuring inconsistency through minimal inconsistent sets, KR 8 (2008) 358–366.

[14]

Fionda V., Greco G., The compl. of LTL on finite traces: Hard and easy fragments, in: Proc. of the 30th AAAI Conference on AI, Phoenix, AAAI, 2016, pp. 971–977.

[15]

G. De Giacomo, R. De Masellis, M. Montali, Reasoning on LTL on finite traces: Insensitivity to infiniteness, in: 28th AAAI Conference on AI, 2014.

[16]

De Giacomo G., Vardi M.Y., Linear temporal logic and linear dynamic logic on finite traces, in: Proceedings of the 23rd IJCAI, Beijing, AAAI, 2013, pp. 854–860.

[17]

Solomakhin D., Montali M., Tessaris S., Masellis R.D., Verification of artifact-centric systems, in: Proceedings of the 11th ICSOC, Springer, 2013, pp. 252–266.

[18]

Hildebrandt T., Mukkamala R.R., Slaats T., Zanitti F., Contracts for cross-organizational workflows as timed dynamic condition response graphs, J. Log. Algebr. Program. 82 (5–7) (2013) 164–185.

[19]

Pill I., Quaritsch T., Behavioral diagnosis of LTL specifications at operator level, in: 23rd International Joint Conference on Artificial Intelligence, Citeseer, 2013.

[20]

Hantry F., Hacid M.-S., Handling conflicts in depth-first search for LTL tableau to debug compliance based languages, 2011, arXiv preprint arXiv:1109.2656.

[21]

Schuppan V., Towards a notion of unsatisfiable and unrealizable cores for LTL, Sci. Comput. Program. 77 (7–8) (2012) 908–939.

[22]

Maggi F.M., Westergaard M., Montali M., van der Aalst W.M., Runtime verification of LTL-based declarative process models, in: Proceedings of the 2nd RV, San Francisco, Springer, 2011, pp. 131–146.

[23]

Grant J., Measuring inconsistency in some branching time logics, J. Appl. Non-Classical Logics 31 (2021) 85–107.

[24]

Vardi M.Y., Branching vs. linear time: Final showdown, in: Proceedings of the 7th TACAS, Italy, Springer, 2001, pp. 1–22.

[25]

Kamide N., Wansing H., Combining linear-time temporal logic with constructiveness and paraconsistency, J. Appl. Log. 8 (2010) 33–61.

[26]

Kamide N., Wansing H., A paraconsistent linear-time temporal logic, Fund. Inform. 106 (2011) 1–23.

[27]

Nute D., Defeasible logic, in: International Conference on Applications of Prolog, Springer, 2001, pp. 151–169.

[28]

Chafik A., Cheikh-Alili F., Condotta J.-F., Varzinczak I., Defeasible linear temporal logic, J. Appl. Non-Classical Logics (2023) 1–51.

[29]

Governatori G., Terenziani P., Temporal extensions to defeasible logic, in: Australasian Joint Conference on Artificial Intelligence, Springer, 2007, pp. 476–485.

[30]

Alman A., Maggi F.M., Montali M., Peñaloza R., Probabilistic declarative process mining, Inf. Syst. 109 (2022).

[31]

Bellodi E., Riguzzi F., Lamma E., Probabilistic declarative process mining, in: International Conference on Knowledge Science, Engineering and Management, Springer, 2010, pp. 292–303.

[32]

Antoniou G., Billington D., Governatori G., Maher M.J., Representation results for defeasible logic, ACM Trans. Comput. Log. 2 (2) (2001) 255–287.

[33]

Mu K., Wang K., Wen L., Approaches to measuring inconsistency for stratified knowledge bases, Internat. J. Approx. Reason. 55 (2) (2014) 529–556.

[34]

I. Kuhlmann, M. Thimm, Algorithms for Inconsistency Measurement using Answer Set Programming, in: Proceedings of the 19th International Workshop on Non-Monotonic Reasoning, NMR, 2021, pp. 159–168.

[35]

F. Chiariello, F.M. Maggi, F. Patrizi, ASP-Based Declarative Process Mining, in: Proceedings of the AAAI Conference on Artificial Intelligence, 2022, pp. 5539–5547.

[36]

Heljanko K., Niemelä I., Bounded LTL model checking with stable models, Theory Pract. Log. Program. 3 (4–5) (2003) 519–550.

[37]

Thimm M., On the expressivity of inconsistency measures, Artificial Intelligence 234 (2016) 120–151.

[38]

Potyka N., Measuring disagreement among knowledge bases, in: International Conference on Scalable Uncertainty Management, Springer, 2018, pp. 212–227.

[39]

Felli P., Gianola A., Montali M., Rivkin A., Winkler S., Conformance checking with uncertainty via SMT, in: International Conference on Business Process Management, Springer, 2022, pp. 199–216.

[40]

Maher M.J., A model-theoretic semantics for defeasible logic, 2002, arXiv preprint cs/0207086.

[41]

Ribeiro J.S., Thimm M., Consolidation via tacit culpability measures: Between explicit and implicit degrees of culpability, KR 2021 (2021) 529–538.

[42]

Shapley L.S., A value for n-person games, in: Contributions To the Theory of Games II, in: Annals of Mathematics Studies, vol. 28, Princeton University Press, 1953, pp. 307–317.

[43]

Pesic M., Schonenberg H., Van der Aalst W.M., Declare: Full support for loosely-structured processes, in: 11th IEEE EDOC, Annapolis, IEEE, 2007, p. 287.

[44]

Burattin A., Maggi F.M., Sperduti A., Conformance checking based on multi-perspective declarative process models, Expert Syst. Appl. 65 (2016) 194–211.

Digital Library

[45]

Kuhlmann I., Thimm M., An algorithm for the contension inconsistency measure using reductions to answer set programming, in: Proceedings of the 14th International Conference on Scalable Uncertainty Management, SUM’20, Springer, 2020, pp. 289–296.

[46]

Kuhlmann I., Gessler A., Laszlo V., Thimm M., A comparison of ASP-based and SAT-based algorithms for the contension inconsistency measure, in: Proceedings of the 15th International Conference on Scalable Uncertainty Management, SUM’22, Springer, 2022.

[47]

Kuhlmann I., Gessler A., Laszlo V., Thimm M., Comparison of SAT-based and ASP-based algorithms for inconsistency measurement, 2023, arXiv preprint arXiv:2304.14832.

[48]

Papadimitriou C., Computational Complexity, Addison-Wesley, 1994.

[49]

Di Ciccio C., Schouten M.H., de Leoni M., Mendling J., Declarative process discovery with minerful in prom., 2015, pp. 60–64.

[50]

A. Alman, C. Di Ciccio, D. Haas, F.M. Maggi, A. Nolte, Rule mining with RuM, in: Int. Conference on Process Mining, 2020, pp. 121–128.

[51]

F.M. Maggi, M. Montali, R. Peñaloza, Temporal logics over finite traces with uncertainty, in: Proceedings of the AAAI Conference on Artificial Intelligence, Vol. 34, No. 06, 2020, pp. 10218–10225.

[52]

Shi H.-X., A quantitative approach for linear temporal logic, in: Quantitative Logic and Soft Computing 2016, Springer, 2017, pp. 49–57.

[53]

Dimitrova R., Ghasemi M., Topcu U., Maximum realizability for linear temporal logic specifications, in: International Symposium on Automated Technology for Verification and Analysis, Springer, 2018, pp. 458–475.

[54]

Thimm M., On the evaluation of inconsistency measures, in: Grant J., Martinez M.V. (Eds.), Measuring Inconsistency in Information, College Publications, 2018.

[55]

De Bona G., Hunter A., Localizing iceberg dependencies, Artificial Intelligence 246 (2017) 118–151.

[56]

Hunter A., Konieczny S., On the measure of conflicts: Shapley inconsistency values, Artificial Intelligence 174 (14) (2010) 1007–1026.

[57]

Brewka G., Eiter T., Truszczynski M., Answer set programming at a glance, Commun. ACM 54 (12) (2011) 92–103.

Digital Library

[58]

Gebser M., Kaminski R., Kaufmann B., Schaub T., Answer set solving in practice, Synth. Lect. Artif. Intell. Mach. Learn. 6 (3) (2012) 1–238.

[59]

Lifschitz V., Answer Set Programming, Springer Berlin, 2019.

[60]

Reiter R., A logic for default reasoning, Artif. Intell. 13 (1–2) (1980) 81–132.

Cited By

Kuhlmann ICorea C(2024)Inconsistency Measurement in LTL Based on Minimal Inconsistent Sets and Minimal Correction SetsScalable Uncertainty Management10.1007/978-3-031-76235-2_17(217-232)Online publication date: 28-Nov-2024
https://dl.acm.org/doi/10.1007/978-3-031-76235-2_17
Fionda VIelo ARicca F(2024)LTLf2ASP: LTLf Bounded Satisfiability in ASPLogic Programming and Nonmonotonic Reasoning10.1007/978-3-031-74209-5_28(373-386)Online publication date: 11-Oct-2024
https://dl.acm.org/doi/10.1007/978-3-031-74209-5_28

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Paraconsistent reasoning for inconsistency measurement in declarative process specifications

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cover image Information Systems

Information Systems Volume 122, Issue C

May 2024

192 pages

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Elsevier Ltd.

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Elsevier Science Ltd.

United Kingdom

Publication History

Published: 01 May 2024

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Cited By

Kuhlmann ICorea C(2024)Inconsistency Measurement in LTL Based on Minimal Inconsistent Sets and Minimal Correction SetsScalable Uncertainty Management10.1007/978-3-031-76235-2_17(217-232)Online publication date: 28-Nov-2024
https://dl.acm.org/doi/10.1007/978-3-031-76235-2_17
Fionda VIelo ARicca F(2024)LTLf2ASP: LTLf Bounded Satisfiability in ASPLogic Programming and Nonmonotonic Reasoning10.1007/978-3-031-74209-5_28(373-386)Online publication date: 11-Oct-2024
https://dl.acm.org/doi/10.1007/978-3-031-74209-5_28

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