Hostname: page-component-8448b6f56d-sxzjt Total loading time: 0 Render date: 2024-04-24T14:59:29.862Z Has data issue: false hasContentIssue false
  • English
  • Français

Relating Two Dialects of Answer Set Programming

Published online by Cambridge University Press:  20 September 2019

AMELIA HARRISON  and
VLADIMIR LIFSCHITZ Open the ORCID record for VLADIMIR LIFSCHITZ [Opens in a new window]
AMELIA HARRISON
Affiliation:
Google (e-mail: amelia.j.harrison@gmail.com)
VLADIMIR LIFSCHITZ
Affiliation:
University of Texas at Austin (e-mail: vl@cs.utexas.edu)
Get access Rights & Permissions [Opens in a new window]

Abstract

The input language of the answer set solver clingo is based on the definition of a stable model proposed by Paolo Ferraris. The semantics of the ASP-Core language, developed by the ASP Standardization Working Group, uses the approach to stable models due to Wolfgang Faber, Nicola Leone, and Gerald Pfeifer. The two languages are based on different versions of the stable model semantics, and the ASP-Core document requires, “for the sake of an uncontroversial semantics,” that programs avoid the use of recursion through aggregates. In this paper we prove that the absence of recursion through aggregates does indeed guarantee the equivalence between the two versions of the stable model semantics, and show how that requirement can be relaxed without violating the equivalence property.

Keywords

Answer set programminganswer set solversstable modelsaggregates
Type
Original Article
Information
Theory and Practice of Logic Programming , Volume 19 , Special Issue 5-6: 35th International Conference on Logic Programming , September 2019 , pp. 1006 - 1020
Copyright
© Cambridge University Press 2019 

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.)

References

Bartholomew, M., Lee, J., and Meng, Y. 2011. First-order extension of the FLP stable model semantics via modified circumscription. In Proceedings of International Joint Conference on Artificial Intelligence (IJCAI). 724–730.Google Scholar
Faber, W., Leone, N., and Pfeifer, G. 2004. Recursive aggregates in disjunctive logic programs: Semantics and complexity. In Proceedings of European Conference on Logics in Artificial Intelligence (JELIA). 200–212.Google Scholar
Faber, W., Pfeifer, G., and Leone, N. 2011. Semantics and complexity of recursive aggregates in answer set programming. Artificial Intelligence 175, 278–298.Google Scholar
Ferraris, P. 2005. Answer sets for propositional theories. In Proceedings of International Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR). 119–131.Google Scholar
Ferraris, P., Lee, J., and Lifschitz, V. 2006. A generalization of the Lin-Zhao theorem. Annals of Mathematics and Artificial Intelligence 47, 79–101.Google Scholar
Gebser, M., Harrison, A., Kaminski, R., Lifschitz, V., and Schaub, T. 2015. Abstract Gringo. Theory and Practice of Logic Programming 15, 449–463.Google Scholar
Gelfond, M. and Zhang, Y. 2014. Vicious circle principle and logic programs with aggregates. Theory and Practice of Logic Programming 14, 4-5, 587–601.CrossRefGoogle Scholar
Harrison, A. 2017. Formal methods for answer set programming. Ph.D. thesis, University of Texas at Austin.Google Scholar
Harrison, A., Lifschitz, V., Pearce, D., and Valverde, A. 2017. Infinitary equilibrium logic and strongly equivalent logic programs. Arificial Intelligence 246, 22–33.Google Scholar
Heyting, A. 1930. Die formalen Regeln der intuitionistischen Logik. Sitzungsberichte der Preussischen Akademie von Wissenschaften. Physikalisch-mathematische Klasse, 42–56.Google Scholar
Truszczynski, M. 2010. Reducts of propositional theories, satisfiability relations, and generalizations of semantics of logic programs. Artificial Intelligence 174, 16, 1285–1306.Google Scholar
Truszczynski, M. 2012. Connecting first-order ASP and the logic FO(ID) through reducts. In Correct Reasoning: Essays on Logic-Based AI in Honor of Vladimir Lifschitz, Erdem, E., Lee, J., Lierler, Y. , and Pearce, D., Eds. Springer, 543–559.Google Scholar