Hostname: page-component-78c5997874-dh8gc Total loading time: 0 Render date: 2024-11-10T17:42:15.189Z Has data issue: false hasContentIssue false
  • English
  • Français

Expressiveness of communication in answer set programming

Published online by Cambridge University Press:  01 November 2011

KIM BAUTERS ,
STEVEN SCHOCKAERT ,
JEROEN JANSSEN ,
DIRK VERMEIR  and
MARTINE DE COCK
KIM BAUTERS
Affiliation:
Department of Applied Mathematics and Computer Science, Krijgslaan 281 (WE02), Universiteit Gent, 9000 Gent, Belgium (e-mail: kim.bauters@ugent.be, steven.schockaert@ugent.be)
STEVEN SCHOCKAERT
Affiliation:
Department of Applied Mathematics and Computer Science, Krijgslaan 281 (WE02), Universiteit Gent, 9000 Gent, Belgium (e-mail: kim.bauters@ugent.be, steven.schockaert@ugent.be)
JEROEN JANSSEN
Affiliation:
Department of Computer Science, Vrije Universiteit Brussel, Pleinlaan 2, 1050 Brussel, Belgium (e-mail: jeroen.janssen@vub.ac.be, dirk.vermeir@vub.ac.be)
DIRK VERMEIR
Affiliation:
Department of Computer Science, Vrije Universiteit Brussel, Pleinlaan 2, 1050 Brussel, Belgium (e-mail: jeroen.janssen@vub.ac.be, dirk.vermeir@vub.ac.be)
MARTINE DE COCK
Affiliation:
Department of Applied Mathematics and Computer Science, Krijgslaan 281 (WE02), Universiteit Gent, 9000 Gent, Belgium (e-mail: martine.decock@ugent.be)
Get access Rights & Permissions [Opens in a new window]

Abstract

Answer set programming (ASP) is a form of declarative programming that allows to succinctly formulate and efficiently solve complex problems. An intuitive extension of this formalism is communicating ASP, in which multiple ASP programs collaborate to solve the problem at hand. However, the expressiveness of communicating ASP has not been thoroughly studied. In this paper, we present a systematic study of the additional expressiveness offered by allowing ASP programs to communicate. First, we consider a simple form of communication where programs are only allowed to ask questions to each other. For the most part, we deliberately consider only simple programs, i.e. programs for which computing the answer sets is in P. We find that the problem of deciding whether a literal is in some answer set of a communicating ASP program using simple communication is NP-hard. In other words, due to the ability of these simple ASP programs to communicate and collaborate, we move up a step in the polynomial hierarchy. Second, we modify the communication mechanism to also allow us to focus on a sequence of communicating programs, where each program in the sequence may successively remove some of the remaining models. This mimics a network of leaders, where the first leader has the first say and may remove models that he or she finds unsatisfactory. Using this particular communication mechanism allows us to capture the entire polynomial hierarchy. This means, in particular, that communicating ASP could be used to solve problems that are above the second level of polynomial hierarchy, such as some forms of abductive reasoning as well as PSPACE-complete problems such as STRIPS planning.

Keywords

logic programminganswer set programmingmulti-agent reasoning
Type
Regular Papers
Information
Theory and Practice of Logic Programming , Volume 13 , Issue 3 , May 2013 , pp. 361 - 394
Copyright
Copyright © Cambridge University Press 2011

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

Baral, C. 2003. Knowledge, Representation, Reasoning and Declarative Problem Solving. Cambridge University Press, Cambridge, UK.CrossRefGoogle Scholar
Bauters, K. 2011. Modeling coalition formation using multi-focused answer sets. In Proceedings of ESSLLI'11 Student Session, Ljubljana, Slovenia, 31 July–11 August. Springer, New York, USA, 25–33.Google Scholar
Bauters, K., Janssen, J., Schockaert, S., Vermeir, D. and DeCock, M. Cock, M. 2010. Communicating answer set programs. In Technical Communications of ICLP 2010. Vol. 7, 34–43. Springer-Verlag, New York, USA.Google Scholar
Bauters, K., Schockaert, S., Vermeir, D. and De Cock, M. In Proceedings of LPNMR'11, Vancouver, British Columbia, Canada. 67–79.Google Scholar
Brain, M. and De Vos, M. 2003. Implementing OCLP as a front-end for answer set solvers: From theory to practice. In Proceedings of ASP'05, Bath, UK. Springer-Verlag New York, USA, 224–238.Google Scholar
Brewka, G. and Eiter, T. 2007. Equilibria in heterogeneous nonmonotonic multi-context systems. In Proceedings of AAAI'07, Vancouver, British Columbia, Canada. AAAI Press, California, USA, 385–390.Google Scholar
Brewka, G., Eiter, T., Fink, M. and Weinzierl, A. 2011. Managed multi-context systems. In Proceedings of IJCAI'11, Barcelona, Catalonia, Spain. AAAI Press, California, USA, 786–791.Google Scholar
Brewka, G., Roelofsen, F. and Serafini, L. 2007. Contextual default reasoning. In Proceedings of IJCAI'07, Hyderabad, India. AAAI Press, California, USA, 268–273.Google Scholar
Buccafurri, F., Caminiti, G. and Laurendi, R. 2008. A logic language with stable model semantics for social reasoning. In Proceedings of ICLP'08, Udine, Italy. Springer-Verlag, New York, USA, 718–723.Google Scholar
Bylander, T. 1994. The computational complexity of propositional STRIPS planning. Artificial Intelligence 69, 165–204.CrossRefGoogle Scholar
Dao-Tran, M., Eiter, T., Fink, M. and Krennwallner, T. 2009. Modular nonmonotonic logic programming revisited. In Proceedings of ICLP'09, Pasadena, California, USA. Springer-Verlag, New York, USA, 145–159.Google Scholar
Dao-Tran, M., Eiter, T., Fink, M. and Krennwallner, T. 2010. Distributed nonmonotonic multi-context systems. In Proceedings of KR'10, Toronto, Canada. AAAI Press, California, USA, 60–70.Google Scholar
Dell'Acqua, P., Sadri, F. and Toni, F. 1999. Communicating agents. In Proceedings of MAS'99, Las Cruces, NM, USA. Pergamon, Netherlands.Google Scholar
De Vos, M., Crick, T., Padget, J., Brain, M., Cliffe, O. and Needham, J. 2005. LAIMA: A multi-agent platform using ordered choice logic programming. In Proceedings of DALT'05. LNCS, vol. 3904. Springer-Verlag, New York, USA, 72–88.Google Scholar
Drescher, C., Eiter, T., Fink, M., Krennwallner, T. and Walsh, T. 2011. Symmetry breaking for distributed multi-context systems. In Proceedings of ICLP'10. Lecture Notes in Computer Science, vol. 6645. Springer-Verlag, New York, USA, 26–39.Google Scholar
Eiter, T., Faber, W., Leone, N. and Pfeifer, G. 1999. The diagnosis frontend of the dlv system. AI Communications 12, 99–111.Google Scholar
Eiter, T. and Gottlob, G. 1995. The complexity of logic-based abduction. Journal of ACM 42, 3–42.Google Scholar
Eiter, T., Ianni, G., Lukasiewicz, T., Schindlauer, R. and Tompits, H. 2008. Combining answer set programming with description logics for the semantic web. Artificial Intelligence 172,12–13, 1495–1539.Google Scholar
Eiter, T., Ianni, G., Schindlauer, R. and Tompits, H. 2005. A uniform integration of higher-order reasoning and external evaluations in answer-set programming. In Proceedings of IJCAI'05, Edinburgh, Scotland. Springer-Verlag, New York, USA, 90–96.Google Scholar
Eiter, T., Ianni, G., Schindlauer, R. and Tompits, H. 2006. dlvhex: A tool for semantic-web reasoning under the answer-set semantics. In Proceedings of International Workshop of ALPSWS'06, Seattle, WA, USA. Springer, New York, USA, 33–39.Google Scholar
Gebser, M., Guziolowski, C., Ivanchev, M., Schaub, T., Siegel, A., Thiele, S. and Veber, P. 2010. Repair and prediction (under inconsistency) in large biological networks with answer set programming. In Proceedings of KR'10, Toronto, Canada. AAAI Press, California, USA, 497–507.Google Scholar
Gelder, A. V., Ross, K. A. and Schlipf, J. S. 1991. The well-founded semantics for general logic programs. Journal of the ACM 38, 3, 620–650.Google Scholar
Gelfond, M. and Lifzchitz, V. 1988. The stable model semantics for logic programming. In Proceedings of ICLP'88, Seattle, Washington. Springer-Verlag, New York, USA, 1081–1086.Google Scholar
Gelfond, M. and Lifschitz, V. 1991. Classical negation in logic programs and disjunctive databases. New Generation Computing 9, 365–385.CrossRefGoogle Scholar
Giunchiglia, F. and Serafini, L. 1994. Multilanguage hierarchical logics or: How we can do without modal logics. Artifial Intelligence 65, 1, 29–70.CrossRefGoogle Scholar
Jeroslow, R. 1985. The polynomial hierarchy and a simple model for competitive analysis. Mathematical Programming 32, 146–164.CrossRefGoogle Scholar
Lifschitz, V. 2002. Answer set programming and plan generation. Artificial Intelligence 138, 39–54.Google Scholar
Lifschitz, V., Tang, L. R. and Turner, H. 1999. Nested expressions in logic programs. Annals of Mathematics and Artificial Intelligence 25, 3–4, 369–389.CrossRefGoogle Scholar
Luo, J., Shi, Z., Wang, M. and Huang, H. 2005. Multi-agent cooperation: A description logic view. In Proceedings of PRIMA'05, Kuala Lumpur, Malaysia. Springer-Verlag, Heidelberg, Germany, 365–379.Google Scholar
Niemelä, I. and Simons, P. 2000. Extending the smodels system with cardinality and weight constraints. In Logic-Based Artificial Intelligence, Minker, J., ed. Kluwer Norwell, MA, USA, 491–521.CrossRefGoogle Scholar
Papadimitriou, C. 1994. Computational Complexity. Addison-Wesley, Boston, MA, USA.Google Scholar
Roelofsen, F. and Serafini, L. 2005. Minimal and absent information in contexts. In Proceedings of IJCAI'05, Edinburgh, Scotland. Springer-Verlag, New York, USA, 558–563.Google Scholar
Tarski, A. 1955. A lattice-theoretical fixpoint theorem and its applications. Pacific Journal of Mathematics 5, 2, 285–309.Google Scholar
Van Nieuwenborgh, D., De Vos, M., Heymans, S. and Vermeir, D. 2007. Hierarchical decision making in multi-agent systems using answer set programming. In Proceedings of CLIMA'07, Helsinki, Finland.Google Scholar