Abstract
In temporal extensions of Answer Set Programming (ASP) based on linear-time, the behavior of dynamic systems is captured by sequences of states. While this representation reflects their relative order, it abstracts away the specific times associated with each state. In many applications, however, timing constraints are important like, for instance, when planning and scheduling go hand in hand. We address this by developing a metric extension of linear-time temporal equilibrium logic, in which temporal operators are constrained by intervals over natural numbers. The resulting Metric Equilibrium Logic provides the foundation of an ASP-based approach for specifying qualitative and quantitative dynamic constraints. To this end, we define a translation of metric formulas into monadic first-order formulas and give a correspondence between their models in Metric Equilibrium Logic and Monadic Quantified Equilibrium Logic, respectively. Interestingly, our translation provides a blue print for implementation in terms of ASP modulo difference constraints.
An extended abstract of this paper appeared in [12].
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References
Aguado, F., Cabalar, P., Diéguez, M., Pérez, G., Vidal, C.: Temporal equilibrium logic: a survey. J. Appl. Non-Class. Log. 23(1–2), 2–24 (2013)
Balduccini, M., Lierler, Y., Woltran, S. (eds.): Proceedings of the Fifteenth International Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR 2019), LNAI, vol. 11481. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-20528-7
Baselice, S., Bonatti, P.A., Gelfond, M.: Towards an integration of answer set and constraint solving. In: Gabbrielli, M., Gupta, G. (eds.) ICLP 2005. LNCS, vol. 3668, pp. 52–66. Springer, Heidelberg (2005). https://doi.org/10.1007/11562931_7
Beck, H., Dao-Tran, M., Eiter, T.: LARS: a logic-based framework for analytic reasoning over streams. Artif. Intell. 261, 16–70 (2018)
Bosser, A., Cabalar, P., Diéguez, M., Schaub, T.: Introducing temporal stable models for linear dynamic logic. In: Proceedings of the Sixteenth International Conference on Principles of Knowledge Representation and Reasoning (KR 2018), pp. 12–21. AAAI Press (2018)
Brzoska, C.: Temporal logic programming with metric and past operators. In: Fisher, M., Owens, R. (eds.) IJCAI 1993. LNCS, vol. 897, pp. 21–39. Springer, Heidelberg (1995). https://doi.org/10.1007/3-540-58976-7_2
Cabalar, P., Diéguez, M., Laferriere, F., Schaub, T.: Implementing dynamic answer set programming over finite traces. In: Proceedings of the Twenty-Fourth European Conference on Artificial Intelligence (ECAI 2020), pp. 656–663. IOS Press (2020)
Cabalar, P., Diéguez, M., Schaub, T.: Towards dynamic answer set programming over finite traces. In: [2], pp. 148–162 (2019)
Cabalar, P., Diéguez, M., Schaub, T., Schuhmann, A.: Towards metric temporal answer set programming. Theory Pract. Logic Program. 20(5), 783–798 (2020)
Cabalar, P., Kaminski, R., Morkisch, P., Schaub, T.: telingo = ASP + Time. In: [2], pp. 256–269 (2019)
Cabalar, P., Kaminski, R., Schaub, T., Schuhmann, A.: Temporal answer set programming on finite traces. Theory Pract. Logic Program. 18(3–4), 406–420 (2018)
Cabalar, P., Diéguez, M., Schaub, T., Schuhmann, A.: Metric temporal answer set programming over timed traces (extended abstract). In: Stream Reasoning Workshop (2021)
De Giacomo, G., Murano, A., Patrizi, F., Perelli, G.: Timed trace alignment with metric temporal logic over finite traces. In: Proceedings of the Eighteenth International Conference on Principles of Knowledge Representation and Reasoning (KR 2022), pp. 227–236. AAAI Press (2020)
Fisher, M., Gabbay, D., Vila, L. (eds.): Handbook of Temporal Reasoning in Artificial Intelligence. Elsevier Science (2005)
Gebser, M., Kaminski, R., Kaufmann, B., Ostrowski, M., Schaub, T., Wanko, P.: Theory solving made easy with Clingo 5. In: Technical Communications of the Thirty-Second International Conference on Logic Programming (ICLP 2016), pp. 2:1–2:15. OASIcs (2016)
Harel, D., Tiuryn, J., Kozen, D.: Dynamic Logic. MIT Press, Cambridge (2000)
Heyting, A.: Die formalen Regeln der intuitionistischen Logik. In: Sitzungsberichte der Preussischen Akademie der Wissenschaften, pp. 42–56. Deutsche Akademie der Wissenschaften zu Berlin (1930)
Hofmann, T., Lakemeyer, G.: A logic for specifying metric temporal constraints for Golog programs. In: Proceedings of the Eleventh Workshop on Cognitive Robotics (CogRob 2018), pp. 36–46. CEUR Workshop Proceedings (2019)
Kamp, J.: Tense logic and the theory of linear order. Ph.D. thesis, University of California at Los Angeles (1968)
Koymans, R.: Specifying real-time properties with metric temporal logic. Real-Time Syst. 2(4), 255–299 (1990)
Lifschitz, V.: Answer set planning. In: Proceedings of the International Conference on Logic Programming (ICLP 1999), pp. 23–37. MIT Press (1999)
Luo, R., Valenzano, R., Li, Y., Beck, C., McIlraith, S.: Using metric temporal logic to specify scheduling problems. In: Proceedings of the Fifteenth International Conference on Principles of Knowledge Representation and Reasoning (KR 2016), pp. 581–584. AAAI Press (2016)
Ouaknine, J., Worrell, J.: On the decidability and complexity of metric temporal logic over finite words. Log. Methods Comput. Sci. 3(1) (2007). https://doi.org/10.2168/LMCS-3(1:8)2007
Pearce, D.: A new logical characterisation of stable models and answer sets. In: Dix, J., Pereira, L.M., Przymusinski, T.C. (eds.) NMELP 1996. LNCS, vol. 1216, pp. 57–70. Springer, Heidelberg (1997). https://doi.org/10.1007/BFb0023801
Pearce, D., Valverde, A.: Quantified equilibrium logic and foundations for answer set programs. In: Garcia de la Banda, M., Pontelli, E. (eds.) ICLP 2008. LNCS, vol. 5366, pp. 546–560. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-89982-2_46
Pnueli, A.: The temporal logic of programs. In: Proceedings of the Eighteenth Symposium on Foundations of Computer Science (FOCS 1977), pp. 46–57. IEEE Computer Society Press (1977)
Son, T., Baral, C., Tuan, L.: Adding time and intervals to procedural and hierarchical control specifications. In: Proceedings of the Nineteenth National Conference on Artificial Intelligence (AAAI 2004), pp. 92–97. AAAI Press (2004)
Wałega, P., Cuenca Grau, B., Kaminski, M., Kostylev, E.: DatalogMTL: computational complexity and expressive power. In: Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence (IJCAI 2019), pp. 1886–1892. ijcai.org (2019)
Wałega, P., Kaminski, M., Cuenca Grau, B.: Reasoning over streaming data in metric temporal Datalog. In: Proceedings of the Thirty-third National Conference on Artificial Intelligence (AAAI 2019), pp. 3092–3099. AAAI Press (2019)
Acknowledgments
This work was supported by MICINN, Spain, grant PID2020-116201GB-I00, Xunta de Galicia, Spain (GPC ED431B 2019/03), Région Pays de la Loire, France (EL4HC and étoiles montantes CTASP), DFG grants SCHA 550/11 and 15, Germany, and European Union COST action CA-17124.
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Cabalar, P., Diéguez, M., Schaub, T., Schuhmann, A. (2022). Metric Temporal Answer Set Programming over Timed Traces. In: Gottlob, G., Inclezan, D., Maratea, M. (eds) Logic Programming and Nonmonotonic Reasoning. LPNMR 2022. Lecture Notes in Computer Science(), vol 13416. Springer, Cham. https://doi.org/10.1007/978-3-031-15707-3_10
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