{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,24]],"date-time":"2026-09-24T22:44:39Z","timestamp":1790289879534,"version":"4.1.0"},"reference-count":26,"publisher":"Cambridge University Press (CUP)","issue":"5","license":[{"start":{"date-parts":[[2020,9,21]],"date-time":"2020-09-21T00:00:00Z","timestamp":1600646400000},"content-version":"unspecified","delay-in-days":20,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":["cambridge.org"],"crossmark-restriction":true},"short-container-title":["Theory and Practice of Logic Programming"],"published-print":{"date-parts":[[2020,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>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.<\/jats:p>","DOI":"10.1017\/s1471068420000307","type":"journal-article","created":{"date-parts":[[2020,9,21]],"date-time":"2020-09-21T05:25:42Z","timestamp":1600665942000},"page":"783-798","update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":10,"title":["Towards Metric Temporal Answer Set Programming"],"prefix":"10.1017","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7440-0953","authenticated-orcid":false,"given":"PEDRO","family":"CABALAR","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3440-4348","authenticated-orcid":false,"given":"MART\u00cdN","family":"DI\u00c9GUEZ","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7456-041X","authenticated-orcid":false,"given":"TORSTEN","family":"SCHAUB","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"ANNA","family":"SCHUHMANN","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2020,9,21]]},"reference":[{"key":"S1471068420000307_ref13","unstructured":"13. Cabalar, P. , Kaminski, R. , Morkisch, P. , and Schaub, T. 2019. telingo = ASP + time. See lpnmr19, 256\u2013269."},{"key":"S1471068420000307_ref10","unstructured":"10. Cabalar, P. 2010. A normal form for linear temporal equilibrium logic. In Proceedings of the Twelfth European Conference on Logics in Artificial Intelligence (JELIA\u201910), Janhunen, T. and Niemel\u00e4, I. , Eds. Springer, 64\u201376."},{"key":"S1471068420000307_ref7","unstructured":"7. Bosser, A. , Cabalar, P. , Di\u00e9guez, 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\u201918), Thielscher, M. , Toni, F. , and Wolter, F. , Eds. AAAI Press, 12\u201321."},{"key":"S1471068420000307_ref20","doi-asserted-by":"publisher","DOI":"10.1007\/BF03037383"},{"key":"S1471068420000307_ref16","unstructured":"16. 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\u201916), Carro, M. and King, A. , Eds. OpenAccess Series in Informatics (OASIcs), 2:1\u20132:15."},{"key":"S1471068420000307_ref5","unstructured":"5. 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\u201916), R. Kambhampati, Ed. IJCAI\/AAAI Press, 929\u2013935."},{"key":"S1471068420000307_ref4","doi-asserted-by":"crossref","unstructured":"4. Balduccini, M. , Lierler, Y. , and Woltran, S. , Eds. 2019. Proceedings of the Fifteenth International Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR\u201919). 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Lifschitz, V. 1999. Answer set planning. In Proceedings of the International Conference on Logic Programming (ICLP\u201999), D. de Schreye, Ed. Press, MIT , 23\u201337."},{"key":"S1471068420000307_ref26","unstructured":"26. 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\u201919), Van Hentenryck, P. and Zhou, Z. , Eds. AAAI Press, 3092\u20133099."},{"key":"S1471068420000307_ref23","unstructured":"23. 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\u201996), Dix, J. , Pereira, L. , and Przymusinski, T. , Eds. Springer, 57\u201370."},{"key":"S1471068420000307_ref19","unstructured":"19. Heyting, A. 1930. Die formalen Regeln der intuitionistischen Logik. In Sitzungsberichte der Preussischen Akademie der Wissenschaften. Deutsche Akademie der Wissenschaften zu Berlin, 42\u201356. Reprint in Logik-Texte: Kommentierte Auswahl zur Geschichte der Modernen Logik, Akademie-Verlag, 1986."},{"key":"S1471068420000307_ref24","unstructured":"24. Pnueli, A. 1977. The temporal logic of programs. In Proceedings of the Eight-teenth Symposium on Foundations of Computer Science (FOCS\u201977). IEEE Computer Society Press, 46\u201357."},{"key":"S1471068420000307_ref15","doi-asserted-by":"publisher","DOI":"10.1016\/0022-0000(79)90046-1"},{"key":"S1471068420000307_ref3","unstructured":"3. Alur, R. and Henzinger, T. 1992. Logics and models of real time: A survey. In Real-Time: Theory in Practice. Springer, 74\u2013106."},{"key":"S1471068420000307_ref6","unstructured":"6. Beck, H. , Dao-Tran, M. , Eiter, T. , and Fink, M. 2015. LARS: A logic-based framework for analyzing reasoning over streams. 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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\u201910). 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