Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-23T12:00:29.778Z Has data issue: false hasContentIssue false
  • English
  • Français

On Uniform Equivalence of Epistemic Logic Programs

Published online by Cambridge University Press:  20 September 2019

WOLFGANG FABER ,
MICHAEL MORAK Open the ORCID record for MICHAEL MORAK [Opens in a new window]  and
STEFAN WOLTRAN
WOLFGANG FABER
Affiliation:
University of Klagenfurt, Austria (e-mails: [email protected], [email protected])
MICHAEL MORAK
Affiliation:
University of Klagenfurt, Austria (e-mails: [email protected], [email protected])
STEFAN WOLTRAN
Affiliation:
TU Wien, Vienna, Austria (e-mail: [email protected])
Get access Rights & Permissions [Opens in a new window]

Abstract

Epistemic Logic Programs (ELPs) extend Answer Set Programming (ASP) with epistemic negation and have received renewed interest in recent years. This led to the development of new research and efficient solving systems for ELPs. In practice, ELPs are often written in a modular way, where each module interacts with other modules by accepting sets of facts as input, and passing on sets of facts as output. An interesting question then presents itself: under which conditions can such a module be replaced by another one without changing the outcome, for any set of input facts? This problem is known as uniform equivalence, and has been studied extensively for ASP. For ELPs, however, such an investigation is, as of yet, missing. In this paper, we therefore propose a characterization of uniform equivalence that can be directly applied to the language of state-of-the-art ELP solvers. We also investigate the computational complexity of deciding uniform equivalence for two ELPs, and show that it is on the third level of the polynomial hierarchy.

Keywords

Logic ProgrammingEpistemic NegationNon-monotonic ReasoningUniform Equivalence
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. 826 - 840
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

Bichler, M., Morak, M., and Woltran, S. 2018. Single-shot epistemic logic program solving. In Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence, IJCAI 2018, July 13-19, 2018, Stockholm, Sweden., J. Lang, Ed. ijcai.org, 1714–1720.Google Scholar
Brewka, G., Eiter, T., and Truszczynski, M. 2011. Answer set programming at a glance. Commun. ACM 54, 12, 92–103.Google Scholar
Cabalar, P., Pearce, D., and Valverde, A. 2007. Minimal logic programs. In Logic Programming, 23rd International Conference, ICLP 2007, Porto, Portugal, September 8-13, 2007, Proceedings, V. Dahl and I. Niemelä, Eds. Lecture Notes in Computer Science, vol. 4670. Springer, 104–118.Google Scholar
Eiter, T. and Fink, M. 2003. Uniform equivalence of logic programs under the stable model semantics. In Proc. ICLP. 224–238.Google Scholar
Eiter, T., Fink, M., Pührer, J., Tompits, H., and Woltran, S. 2013. Model-based recasting in answer-set programming. Journal of Applied Non-Classical Logics 23, 1-2, 75–104.Google Scholar
Eiter, T., Fink, M., Tompits, H., and Woltran, S. 2004. Simplifying logic programs under uniform and strong equivalence. In Proc. LPNMR. 87–99.Google Scholar
Eiter, T., Fink, M., Tompits, H., and Woltran, S. 2005. Strong and uniform equivalence in answer-set programming: Characterizations and complexity results for the non-ground case. In Proc. AAAI. 695–700.Google Scholar
Eiter, T. and Gottlob, G. 1995. On the computational cost of disjunctive logic programming: Propositional case. Ann. Math. Artif. Intell. 15, 3-4, 289–323.Google Scholar
Faber, W., Morak, M., and Woltran, S. 2019. Strong equivalence for epistemic logic programs made easy. In Proc. AAAI.Google Scholar
Fariñas del Cerro, L., Herzig, A., and Su, E. I. 2015. Epistemic equilibrium logic. In Proceedings of the Twenty-Fourth International Joint Conference on Artificial Intelligence, IJCAI 2015, Buenos Aires, Argentina, July 25-31, 2015, Q. Yang and M. Wooldridge, Eds. AAAI Press, 2964–2970.Google Scholar
Gebser, M., Kaminski, R., Kaufmann, B., and Schaub, T. 2012. Answer Set Solving in Practice. Morgan & Claypool.Google Scholar
Gelfond, M. 1991. Strong introspection. In Proceedings of the 9th National Conference on Artificial Intelligence, Anaheim, CA, USA, July 14-19, 1991, Volume 1, T. L. Dean and K. R. McKeown, Eds. AAAI Press / The MIT Press, 386–391.Google Scholar
Gelfond, M. 1994. Logic programming and reasoning with incomplete information. Ann. Math. Artif. Intell. 12, 1-2, 89–116.Google Scholar
Gelfond, M. 2011. New semantics for epistemic specifications. In Logic Programming and Nonmonotonic Reasoning - 11th International Conference, LPNMR 2011, Vancouver, Canada, May 16-19, 2011. Proceedings, J. P. Delgrande and W. Faber, Eds. Lecture Notes in Computer Science, vol. 6645. Springer, 260–265.Google Scholar
Gelfond, M. and Lifschitz, V. 1988. The stable model semantics for logic programming. In Logic Programming, Proceedings of the Fifth International Conference and Symposium, Seattle, Washington, USA, August 15-19, 1988 (2 Volumes), R. A. Kowalski and K. A. Bowen, Eds. MIT Press, 1070–1080.Google Scholar
Gelfond, M. and Lifschitz, V. 1991. Classical negation in logic programs and disjunctive databases. New Generation Comput. 9, 3/4, 365–386.Google Scholar
Janhunen, T., Oikarinen, E., Tompits, H., and Woltran, S. 2009. Modularity aspects of disjunctive stable models. J. Artif. Intell. Res. 35, 813–857.Google Scholar
Kahl, P. T. 2014. Refining the semantics for epistemic logic programs. Ph.D. thesis, Texas Tech University, Texas, USA.Google Scholar
Kahl, P. T., Watson, R., Balai, E., Gelfond, M., and Zhang, Y. 2015. The language of epistemic specifications (refined) including a prototype solver. J. Log. Comput. 25.Google Scholar
Lifschitz, V., Pearce, D., and Valverde, A. 2001. Strongly equivalent logic programs. ACM Trans. Comput. Log. 2, 4, 526–541.Google Scholar
Lifschitz, V., Tang, L. R., and Turner, H. 1999. Nested expressions in logic programs. Ann. Math. Artif. Intell. 25, 3-4, 369–389.Google Scholar
Lifschitz, V. and Turner, H. 1994. Splitting a logic program. In Proc. ICLP. 23–37.Google Scholar
Lin, F. and Chen, Y. 2007. Discovering classes of strongly equivalent logic programs. J. Artif. Intell. Res. 28, 431–451.Google Scholar
Maher, M. J. 1988. Equivalences of Logic Programs. In Foundations of Deductive Databases and Logic Programming, Minker, J., Ed. Morgan Kaufmann Publishers, Inc., Washington DC, 627–658.Google Scholar
Oikarinen, E. 2007. Modular answer set programming. In Proc. ICLP. 462–463.Google Scholar
Pearce, D., Tompits, H., and Woltran, S. 2009. Characterising equilibrium logic and nested logic programs: Reductions and complexity. TPLP 9, 5, 565–616.Google Scholar
Sagiv, Y. 1988. Optimizing Datalog Programs. In Foundations of Deductive Databases and Logic Programming, Minker, J., Ed. Morgan Kaufmann Publishers, Inc., Washington DC, 659–698.Google Scholar
Schaub, T. and Woltran, S. 2018. Special issue on answer set programming. KI 32, 2–3.Google Scholar
Shen, Y. and Eiter, T. 2016. Evaluating epistemic negation in answer set programming. Artif. Intell. 237, 115–135.Google Scholar
Son, T. C., Le, T., Kahl, P. T., and Leclerc, A. P. 2017. On computing world views of epistemic logic programs. In Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence, IJCAI 2017, Melbourne, Australia, August 19-25, 2017, Sierra, C., Ed. ijcai.org, 1269–1275.Google Scholar
Truszczynski, M. 2011. Revisiting epistemic specifications. In Logic Programming, Knowledge Representation, and Nonmonotonic Reasoning - Essays Dedicated to Michael Gelfond on the Occasion of His 65th Birthday.Google Scholar
Turner, H. 2003. Strong equivalence made easy: nested expressions and weight constraints. TPLP 3, 4-5, 609–622.Google Scholar
Wang, K. and Zhang, Y. 2005. Nested epistemic logic programs. In Logic Programming and Nonmonotonic Reasoning, 8th International Conference, LPNMR 2005, Diamante, Italy, September 5-8, 2005, Proceedings, C. Baral, G. Greco, N. Leone, and G. Terracina, Eds. LNCS, vol. 3662. Springer, 279–290.Google Scholar