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Modeling and Reasoning in Event Calculus using Goal-Directed Constraint Answer Set Programming

Published online by Cambridge University Press:  02 November 2021

JOAQUÍN ARIAS Open the ORCID record for JOAQUÍN ARIAS [Opens in a new window] ,
MANUEL CARRO ,
ZHUO CHEN  and
GOPAL GUPTA
JOAQUÍN ARIAS
Affiliation:
CETINIA, Universidad Rey Juan Carlos, Madrid, Spain (e-mail: [email protected])
MANUEL CARRO
Affiliation:
IMDEA Software Institute, Madrid, Spain Universidad Politécnica de Madrid, Madrid, Spain (e-mails: [email protected], [email protected])
ZHUO CHEN
Affiliation:
University of Texas at Dallas, Richardson, USA (e-mail: [email protected])
GOPAL GUPTA
Affiliation:
University of Texas at Dallas, Richardson, USA (e-mail: [email protected])
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Abstract

Automated commonsense reasoning (CR) is essential for building human-like AI systems featuring, for example, explainable AI. Event calculus (EC) is a family of formalisms that model CR with a sound, logical basis. Previous attempts to mechanize reasoning using EC faced difficulties in the treatment of the continuous change in dense domains (e.g. time and other physical quantities), constraints among variables, default negation, and the uniform application of different inference methods, among others. We propose the use of s(CASP), a query-driven, top-down execution model for Predicate Answer Set Programming with Constraints, to model and reason using EC. We show how EC scenarios can be naturally and directly encoded in s(CASP) and how it enables deductive and abductive reasoning tasks in domains featuring constraints involving both dense time and dense fluents.

Keywords

event calculusconstraintsASPcommonsense reasoning
Type
Original Article
Information
Theory and Practice of Logic Programming , Volume 22 , Issue 1 , January 2022 , pp. 51 - 80
Copyright
© The Author(s), 2021. Published by Cambridge University Press

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Footnotes

*

This paper is an extended version of the work by Arias et al. (2019)

†

Work partially supported by EIT Digital, MICINN projects RTI2018-095390-B-C33 InEDGEMobility (MCIU/AEI/FEDER, UE), PID2019-108528RB-C21 ProCode, Comunidad de Madrid project S2018/TCS-4339 BLOQUES-CM co-funded by EIE Funds of the European Union, US NSF Grants IIS 1718945, IIS 1910131, IIP 1916206.

References

Arias, J. and Carro, M. 2019. Description, implementation, and evaluation of a generic design for tabled CLP. Theory and Practice of Logic Programming 19, 3 (May), 412–448.CrossRefGoogle Scholar
Arias, J., Carro, M., Salazar, E., Marple, K. and Gupta, G. 2018. Constraint Answer Set Programming without Grounding. Theory and Practice of Logic Programming 18, 3–4, 337–354.CrossRefGoogle Scholar
Arias, J., Chen, Z., Carro, M. and Gupta, G. 2019. Modeling and reasoning in event calculus using goal-directed constraint answer set programming. In Pre-Proc. of the 29th Int’l. Symposium on Logic-based Program Synthesis and Transformation.CrossRefGoogle Scholar
Bartholomew, M. and Lee, J. 2014. System aspmt2smt: Computing ASPMT Theories by SMT Solvers. In 14th European Conference on Logics in Artificial Intelligence. LNCS, vol. 8761. Springer, 529–542.Google Scholar
Chittaro, L. and Montanari, A. 1996. Efficient Temporal Reasoning in the Cached Event Calculus. Computational Intelligence 12, 359–382.CrossRefGoogle Scholar
Clark, K. L. 1978. Negation as Failure. In Logic and Data Bases, Gallaire, H. and Minker, J., Eds. Springer, 293–322.CrossRefGoogle Scholar
de Moura, L. M. and Bjørner, N. 2008. Z3: An efficient SMT solver. In Tools and Algorithms for the Construction and Analysis of Systems, 14th International Conference, TACAS 2008, Ramakrishnan, C. R. and Rehof, J., Eds. Lecture Notes in Computer Science, vol. 4963. Springer, 337–340.Google Scholar
Dovier, A., Pontelli, E. and Rossi, G. 2000. A necessary condition for constructive negation in constraint logic programming. Information Processing Letters 74, 3–4, 147–156.CrossRefGoogle Scholar
Erdem, E. and Lifschitz, V. 2003. Tight logic programs. Theory and Practice of Logic Programming 3, 4–5, 499–518.CrossRefGoogle Scholar
Ferraris, P., Lee, J. and Lifschitz, V. 2011. Stable models and circumscription. Artificial Intelligence 175, 1, 236–263.CrossRefGoogle Scholar
Gebser, M., Kaminski, R., Kaufmann, B. and Schaub, T. 2014. Clingo = ASP + Control: Preliminary Report. arXiv 1405.3694. Google Scholar
Gelfond, M. and Lifschitz, V. 1988. The stable model semantics for logic programming. In 5th International Conference on Logic Programming, 1070–1080.Google Scholar
Gupta, G., Bansal, A., Min, R., Simon, L. and Mallya, A. 2007. Coinductive Logic Programming and its Applications. In 23rd Int’l. Conference on Logic Programming. Springer, 27–44.Google Scholar
Hall, B., Varanasi, S. C., Fiedor, J., Arias, J., Basu, K., Li, F., Bhatt, D., Driscoll, K., Salazar, E. and Gupta, G. 2021. Knowledge-assisted reasoning of model-augmented system requirements with event calculus and goal-directed answer set programming. In Proc. 8th Workshop on Horn Clause Verification and Synthesis.CrossRefGoogle Scholar
Hermenegildo, M. V., Bueno, F., Carro, M., Lopez-Garcia, P., Mera, E., Morales, J. and Puebla, G. 2012. An overview of ciao and its design philosophy. Theory and Practice of Logic Programming 12, 1–2 (January), 219–252.CrossRefGoogle Scholar
Holzbaur, C. 1995. OFAI CLP(Q,R) Manual, Edition 1.3.3. Tech. Rep. TR-95-09, Austrian Research Institute for Artificial Intelligence, Vienna.Google Scholar
Kowalski, R. and Sergot, M. 1989. A logic-based calculus of events. In Foundations of Knowledge Base Management. Springer, 23–55.CrossRefGoogle Scholar
Lee, J. and Meng, Y. 2013. Answer set programming modulo theories and reasoning about continuous changes. In 23rd Int’l. Joint Conference on Artificial Intelligence. 990–996.Google Scholar
Lee, J. and Palla, R. 2012. Reformulating the situation calculus and the event calculus in the general theory of stable models and in answer set programming. Journal of Artificial Intelligence Research 43, 571–620.CrossRefGoogle Scholar
Lee, J. and Palla, R. 2020. F2LP: Computing answer sets of first order formulas. https://github.com/azreasoners/F2LP. Accessed on October, 2020.Google Scholar
Lifschitz, V. 1985. Computing circumscription. In Proceedings of the 9th International Joint Conference on Artificial Intelligence. Los Angeles, CA, USA, August 1985. 121–127.Google Scholar
Lifschitz, V. 1999. Action Languages, Answer Sets, and Planning. Springer Berlin Heidelberg, 357–373.Google Scholar
Lifschitz, V., Pearce, D. and Valverde, A. 2001. Strongly Equivalent Logic Programs. ACM Transactions on Computational Logic 2, 4, 526–541.CrossRefGoogle Scholar
Marek, V. W. and Truszczynski, M. 1999. Stable Models and an Alternative Logic Programming Paradigm. In The Logic Programming Paradigm: a 25-Year Perspective. Springer-Verlag, 375–398.CrossRefGoogle Scholar
Marple, K., Bansal, A., Min, R. and Gupta, G. 2012. Goal-directed execution of answer set programs. In Principles and Practice of Declarative Programming, PPDP’12, Leuven, Belgium - September 19 - 21, 2012, Schreye, D. D., Janssens, G., and King, A., Eds. ACM, 35–44.Google Scholar
Marple, K. and Gupta, G. 2014. Dynamic consistency checking in goal-directed answer set programming. Theory and Practice of Loging Programming 14, 4–5, 415–427.CrossRefGoogle Scholar
Marple, K., Salazar, E. and Gupta, G. 2017. Computing stable models of normal logic programs without grounding. arXiv 1709.00501. Google Scholar
Marriott, K. and Stuckey, P. J. 1998. Programming with Constraints: An Introduction. MIT Press.CrossRefGoogle Scholar
Marriott, K., Stuckey, P. J. and Wallace, M. 2006. Constraint logic programming. In Foundations of Artificial Intelligence. Vol. 2. Elsevier, 409–452.Google Scholar
McCarthy, J. 1980. Circumscription - A form of non-monotonic reasoning. Artificial Intelligence 13, 1–2, 27–39.CrossRefGoogle Scholar
Mellarkod, V. S., Gelfond, M. and Zhang, Y. 2008a. Integrating answer set programming and constraint logic programming. Annals of Mathematics and Artificial Intelligence 53, 1–4, 251–287.CrossRefGoogle Scholar
Mellarkod, V. S., Gelfond, M. and Zhang, Y. 2008b. Integrating answer set programming and constraint logic programming. Tech. rep., Texas Tech University. October. This is a long version of (Mellarkod et al. 2008a), available at https://www.depts.ttu.edu/cs/research/documents/46.pdf.Google Scholar
Mueller, E. T. 2008a. Chapter 17: Event calculus. In Handbook of Knowledge Representation, van Harmelen, F., Lifschitz, V., and Porter, B., Eds. Foundations of AI, vol. 3. Elsevier, 671–708.Google Scholar
Mueller, E. T. 2008b. Discrete event calculus reasoner documentation. Software documentation, IBM Thomas J. Watson Research Center, PO Box 704. Available at: http://decreasoner.sourceforge.net/. Accessed on October, 2020.Google Scholar
Mueller, E. T. 2014. Commonsense Reasoning: An Event Calculus Based Approach. Morgan Kaufmann.Google Scholar
Shanahan, M. 1999. The event calculus explained. In Artificial Intelligence Today. Springer, 409–430.Google Scholar
Shanahan, M. 2000. An abductive event calculus planner. The Journal of Logic Programming 44, 1–3, 207–240.CrossRefGoogle Scholar
Stuckey, P. 1991. Constructive negation for constraint logic programming. In Proc. LICS’91, 328–339.Google Scholar
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