Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-18T08:34:37.206Z Has data issue: false hasContentIssue false
  • English
  • Français

Towards Metric Temporal Answer Set Programming

Published online by Cambridge University Press:  21 September 2020

PEDRO CABALAR Open the ORCID record for PEDRO CABALAR [Opens in a new window] ,
MARTÍN DIÉGUEZ Open the ORCID record for MARTÍN DIÉGUEZ [Opens in a new window] ,
TORSTEN SCHAUB Open the ORCID record for TORSTEN SCHAUB [Opens in a new window]  and
ANNA SCHUHMANN
PEDRO CABALAR
Affiliation:
University of Corunna, Spain
MARTÍN DIÉGUEZ
Affiliation:
LERIA, Université d’Angers, France
TORSTEN SCHAUB
Affiliation:
University of Potsdam, Germany
ANNA SCHUHMANN
Affiliation:
University of Potsdam, Germany
Get access Rights & Permissions [Opens in a new window]

Abstract

We elaborate upon the theoretical foundations of a metric temporal extension of Answer Set Programming. In analogy to previous extensions of ASP with constructs from Linear Temporal and Dynamic Logic, we accomplish this in the setting of the logic of Here-and-There and its non-monotonic extension, called Equilibrium Logic. More precisely, we develop our logic on the same semantic underpinnings as its predecessors and thus use a simple time domain of bounded time steps. This allows us to compare all variants in a uniform framework and ultimately combine them in a common implementation.

Type
Original Article
Information
Theory and Practice of Logic Programming , Volume 20 , Issue 5: 36th International Conference on Logic Programming Special Issue I , September 2020 , pp. 783 - 798
Check for updates
Copyright
© The Author(s), 2020. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

*

Partially supported by MINECO, Spain, grant TIC2017-84453-P.

References

Aguado, F., Cabalar, P., Diéguez, M., Pérez, G., and Vidal, C. 2013. Temporal equilibrium logic: a survey. Journal of Applied Non-Classical Logics 23, 1-2, 2–24.Google Scholar
Allen, J. 1983. Maintaining knowledge about temporal intervals. Communications of the ACM 26, 11, 832–843.CrossRefGoogle Scholar
Alur, R. and Henzinger, T. 1992. Logics and models of real time: A survey. In Real-Time: Theory in Practice. Springer, 74–106.Google Scholar
Balduccini, M., Lierler, Y., and Woltran, S., Eds. 2019. Proceedings of the Fifteenth International Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR’19). Springer.Google Scholar
Beck, H., Dao-Tran, M., and Eiter, T. 2016. Equivalent stream reasoning programs. In Proceedings of the Twenty-fifth International Joint Conference on Artificial Intelligence (IJCAI’16), R. Kambhampati, Ed. IJCAI/AAAI Press, 929–935.Google Scholar
Beck, H., Dao-Tran, M., Eiter, T., and Fink, M. 2015. LARS: A logic-based framework for analyzing reasoning over streams. In Proceedings of the Twenty-Ninth National Conference on Artificial Intelligence (AAAI’15), Bonet, B. and Koenig, S., Eds. AAAI Press, 1431–1438.Google Scholar
Bosser, A., Cabalar, P., Diéguez, M., and Schaub, T. 2018. Introducing temporal stable models for linear dynamic logic. In Proceedings of the Sixteenth International Conference on Principles of Knowledge Representation and Reasoning (KR’18), Thielscher, M., Toni, F., and Wolter, F., Eds. AAAI Press, 12–21.Google Scholar
Brandt, S., Kalayci, E., Ryzhikov, V., Xiao, G., and Zakharyaschev, M. 2018. Querying log data with metric temporal logic. Journal of Artificial Intelligence Research 62, 829–877.CrossRefGoogle Scholar
Brzoska, C. 1995. Temporal logic programming with metric and past operators. In Proceedings of the Workshop on Executable Modal and Temporal Logics, Fisher, M. and Owens, R., Eds. Springer, 21–39.Google Scholar
Cabalar, P. 2010. A normal form for linear temporal equilibrium logic. In Proceedings of the Twelfth European Conference on Logics in Artificial Intelligence (JELIA’10), Janhunen, T. and Niemelä, I., Eds. Springer, 64–76.Google Scholar
Cabalar, P., Diéguez, M., Laferriere, F., and Schaub, T. 2020. Implementing dynamic answer set programming over finite traces. In Proceedings of the Twenty-fourth European Conference on Artificial Intelligence (ECAI’20), G. De Giacomo, Ed. Press, IOS. To appear.Google Scholar
Cabalar, P., Diéguez, M., and Schaub, T. 2019. Towards dynamic answer set programming over finite traces. See lpnmr19, 148–162.Google Scholar
Cabalar, P., Kaminski, R., Morkisch, P., and Schaub, T. 2019. telingo = ASP + time. See lpnmr19, 256–269.Google Scholar
Cabalar, P., Kaminski, R., Schaub, T., and Schuhmann, A. 2018. Temporal answer set programming on finite traces. Theory and Practice of Logic Programming 18, 3-4, 406–420.Google Scholar
Fischer, M. and Ladner, R. 1979. Propositional dynamic logic of regular programs. Journal of Computer and System Sciences 18, 2, 194–211.CrossRefGoogle Scholar
Gebser, M., Kaminski, R., Kaufmann, B., Ostrowski, M., Schaub, T., and Wanko, P. 2016. Theory solving made easy with clingo 5. In Technical Communications of the Thirty-second International Conference on Logic Programming (ICLP’16), Carro, M. and King, A., Eds. OpenAccess Series in Informatics (OASIcs), 2:1–2:15.Google Scholar
Gödel, K. 1932. Zum intuitionistischen Aussagenkalkül. Anzeiger der Akademie der Wissenschaften in Wien, 65–66.Google Scholar
Harel, D., Tiuryn, J., and Kozen, D. 2000. Dynamic Logic. MIT Press.Google Scholar
Heyting, A. 1930. Die formalen Regeln der intuitionistischen Logik. In Sitzungsberichte der Preussischen Akademie der Wissenschaften. Deutsche Akademie der Wissenschaften zu Berlin, 42–56. Reprint in Logik-Texte: Kommentierte Auswahl zur Geschichte der Modernen Logik, Akademie-Verlag, 1986.Google Scholar
Kowalski, R. and Sergot, M. 1986. A logic-based calculus of events. New Generation Computing 4, 1, 67–95.CrossRefGoogle Scholar
Lifschitz, V. 1999. Answer set planning. In Proceedings of the International Conference on Logic Programming (ICLP’99), D. de Schreye, Ed. Press, MIT, 23–37.Google Scholar
Ouaknine, J. and Worrell, J. 2005. On the decidability of metric temporal logic. In Proceedings of the Twentieth Annual Symposium on Logic in Computer Science (LICS’10). IEEE Computer Society Press, 188–197.Google Scholar
Pearce, D. 1997. A new logical characterisation of stable models and answer sets. In Proceedings of the Sixth International Workshop on Non-Monotonic Extensions of Logic Programming (NMELP’96), Dix, J., Pereira, L., and Przymusinski, T., Eds. Springer, 57–70.Google Scholar
Pnueli, A. 1977. The temporal logic of programs. In Proceedings of the Eight-teenth Symposium on Foundations of Computer Science (FOCS’77). IEEE Computer Society Press, 46–57.Google Scholar
Son, T., Baral, C., and Tuan, L. 2004. Adding time and intervals to procedural and hierarchical control specifications. In Proceedings of the Nineteenth National Conference on Artificial Intelligence (AAAI’04), McGuinness, D. and Ferguson, G., Eds. AAAI Press, 92–97.Google Scholar
Walega, P., Kaminski, M., and Cuenca Grau, B. 2019. Reasoning over streaming data in metric temporal datalog. In Proceedings of the Thirty-third National Conference on Artificial Intelligence (AAAI’19), Van Hentenryck, P. and Zhou, Z., Eds. AAAI Press, 3092–3099.Google Scholar