Hostname: page-component-78c5997874-lj6df Total loading time: 0 Render date: 2024-11-10T21:18:10.306Z Has data issue: false hasContentIssue false
  • English
  • Français

Stable models for infinitary formulas with extensional atoms

Published online by Cambridge University Press:  14 October 2016

AMELIA HARRISON  and
VLADIMIR LIFSCHITZ
AMELIA HARRISON
Affiliation:
University of Texas, Austin, Texas, USA (e-mail: ameliaj@cs.utexas.edu, vl@cs.utexas.edu)
VLADIMIR LIFSCHITZ
Affiliation:
University of Texas, Austin, Texas, USA (e-mail: ameliaj@cs.utexas.edu, vl@cs.utexas.edu)
Get access Rights & Permissions [Opens in a new window]

Abstract

The definition of stable models for propositional formulas with infinite conjunctions and disjunctions can be used to describe the semantics of answer set programming languages. In this note, we enhance that definition by introducing a distinction between intensional and extensional atoms. The symmetric splitting theorem for first-order formulas is then extended to infinitary formulas and used to reason about infinitary definitions.

Type
Regular Papers
Information
Theory and Practice of Logic Programming , Volume 16 , Special Issue 5-6: 32nd International Conference on Logic Programming , September 2016 , pp. 771 - 786
Copyright
Copyright © Cambridge University Press 2016 

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

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. 2007. A logic program characterization of causal theories. In Proceedings of International Joint Conference on Artificial Intelligence (IJCAI), 366–371.Google Scholar
Ferraris, P., Lee, J. and Lifschitz, V. 2007. A new perspective on stable models. In Proceedings of International Joint Conference on Artificial Intelligence (IJCAI), 372–379.Google Scholar
Ferraris, P., Lee, J. and Lifschitz, V. 2011. Stable models and circumscription. Artificial Intelligence 175, 236–263.Google Scholar
Ferraris, P., Lee, J., Lifschitz, V. and Palla, R. 2009. Symmetric splitting in the general theory of stable models. In Proceedings of International Joint Conference on Artificial Intelligence (IJCAI), 797–803.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 Lifschitz, V. 1988. The stable model semantics for logic programming. In Proceedings of International Logic Programming Conference and Symposium, Kowalski, R. and Bowen, K., Eds. MIT Press, 1070–1080.Google Scholar
Gelfond, M. and Przymusinska, H. 1996. Towards a theory of elaboration tolerance: Logic programming approach. International Journal of Software Engineering and Knowledge Engineering 6, 1, 89–112.CrossRefGoogle Scholar
Harrison, A., Lifschitz, V., Pearce, D. and Valverde, A. 2015. Infinitary equilibrium logic and strong equivalence. In Proceedings of International Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR), 398–410.Google Scholar
Lierler, Y. and Truszczynski, M. 2011. Transition systems for model generators — a unifying approach. Theory and Practice of Logic Programming, 27th International Conference on Logic Programming (ICLP) Special Issue 11, issue 4–5.Google Scholar
Lifschitz, V. and Yang, F. 2012. Lloyd-Topor completion and general stable models. In Working Notes of the 5th Workshop of Answer Set Programming and Other Computing Paradigms (ASPOCP).Google Scholar
Oikarinen, E. and Janhunen, T. 2008. Achieving compositionality of the stable model semantics for Smodels programs. Theory and Practice of Logic Programming 5–6, 717–761.CrossRefGoogle 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