Binary Frontier-Guarded ASP with Function Symbols

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9202)

Abstract

It has been acknowledged that emerging Web applications require features that are not available in standard rule languages like Datalog or Answer Set Programming (ASP), e.g., they are not powerful enough to deal with anonymous values (objects that are not explicitly mentioned in the data but whose existence is implied by the background knowledge). In this paper, we introduce a new rule language based on ASP extended with function symbols, which can be used to reason about anonymous values. In particular, we define binary frontier-guarded programs (BFG programs) that allow for disjunction, function symbols, and negation under the stable model semantics. In order to ensure decidability, BFG programs are syntactically restricted by allowing at most binary predicates and by requiring rules to be frontier-guarded. BFG programs are expressive enough to simulate ontologies expressed in popular Description Logics (DLs), capture their recent non-monotonic extensions, and can simulate conjunctive query answering over many standard DLs. We provide an elegant automata-based algorithm to reason in BFG programs, which yields a 3ExpTime upper bound for reasoning tasks like deciding consistency or cautious entailment. Due to existing results, these problems are known to be 2ExpTime-hard.

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References

  1. 1.
    Abiteboul, S., Vianu, V.: Datalog extensions for database queries and updates. Journal of Computer and System Sciences 43(1), 62–124 (1991)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Andréka, H., Németi, I.: The generalised completeness of Horn predicate logics as programming language. Acta Cybernetica 4(1), 3–10 (1978)MathSciNetGoogle Scholar
  3. 3.
    Baget, J., Garreau, F., Mugnier, M., Rocher, S.: Revisiting chase termination for existential rules and their extension to nonmonotonic negation. CoRR abs/1405.1071 (2014)Google Scholar
  4. 4.
    Baget, J., Leclère, M., Mugnier, M., Salvat, E.: On rules with existential variables: Walking the decidability line. Artif. Intell. 175(9–10), 1620–1654 (2011)CrossRefGoogle Scholar
  5. 5.
    Baget, J., Mugnier, M., Rudolph, S., Thomazo, M.: Walking the complexity lines for generalized guarded existential rules. In: Proc. of IJCAI 2011. IJCAI/AAAI (2011)Google Scholar
  6. 6.
    Baselice, S., Bonatti, P.A., Criscuolo, G.: On finitely recursive programs. Theory and Practice of Logic Programming 9(2), 213–238 (2009)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Bonatti, P.A.: Reasoning with infinite stable models. Artificial Intelligence 156(1), 75–111 (2004)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Calautti, M., Greco, S., Molinaro, C., Trubitsyna, I.: Checking termination of logic programs with function symbols through linear constraints. In: Bikakis, A., Fodor, P., Roman, D. (eds.) RuleML 2014. LNCS, vol. 8620, pp. 97–111. Springer, Heidelberg (2014) Google Scholar
  9. 9.
    Calì, A., Gottlob, G., Kifer, M.: Taming the infinite chase: Query answering under expressive relational constraints. J. Artif. Intell. Res. (JAIR) 48, 115–174 (2013)Google Scholar
  10. 10.
    Calimeri, F., Cozza, S., Ianni, G., Leone, N.: Computable functions in ASP: theory and implementation. In: de la Banda, M.G., Pontelli, E. (eds.) ICLP 2008. LNCS, vol. 5366, pp. 407–424. Springer, Heidelberg (2008) CrossRefGoogle Scholar
  11. 11.
    Calvanese, D., Eiter, T., Ortiz, M.: Answering regular path queries in expressive description logics via alternating tree-automata. Inf. Comput. 237, 12–55 (2014)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Courcelle, B., Engelfriet, J.: Graph Structure and Monadic Second-Order Logic - A Language-Theoretic Approach, Encyclopedia of mathematics and its applications, vol. 138. Cambridge University Press (2012)Google Scholar
  13. 13.
    Eiter, T., Šimkus, M.: Bidirectional answer set programs with function symbols. In: Boutilier, C. (ed.) Proc. of IJCAI 2009, pp. 765–771 (2009)Google Scholar
  14. 14.
    Eiter, T., Šimkus, M.: FDNC: decidable nonmonotonic disjunctive logic programs with function symbols. ACM Trans. Comput. Log. 11(2) (2010)Google Scholar
  15. 15.
    Emerson, E.A., Jutla, C.S.: The complexity of tree automata and logics of programs (extended abstract). In: Proc. of FOCS 1988, pp. 328–337. IEEE (1988)Google Scholar
  16. 16.
    Feier, C., Heymans, S.: Reasoning with forest logic programs and f-hybrid knowledge bases. TPLP 13(3), 395–463 (2013)MathSciNetGoogle Scholar
  17. 17.
    Gelfond, M., Lifschitz, V.: Classical negation in logic programs and disjunctive databases. New Generation Computing 9(3/4), 365–386 (1991)CrossRefGoogle Scholar
  18. 18.
    Gottlob, G., Hernich, A., Kupke, C., Lukasiewicz, T.: Stable model semantics for guarded existential rules and description logics. In: Proc. of KR 2014. AAAI Press (2014)Google Scholar
  19. 19.
    Gottlob, G., Rudolph, S., Šimkus, M.: Expressiveness of guarded existential rule languages. In: Proc. of PODS 2014, pp. 27–38. ACM (2014)Google Scholar
  20. 20.
    Greco, S., Molinaro, C., Trubitsyna, I.: Bounded programs: a new decidable class of logic programs with function symbols. In: Proc. of IJCAI 2013. IJCAI/AAAI (2013)Google Scholar
  21. 21.
    Hull, R., Yoshikawa, M.: Ilog: declarative creation and manipulation of object identifiers. In: Proc. of VLDB 1990. Morgan Kaufmann Publishers Inc. (1990)Google Scholar
  22. 22.
    Lutz, C.: Inverse roles make conjunctive queries hard. In: Proc. of DL 2007. CEUR Workshop Proceedings, vol. 250. CEUR-WS.org (2007)Google Scholar
  23. 23.
    Magka, D., Krötzsch, M., Horrocks, I.: Computing stable models for nonmonotonic existential rules. In: Proc. of IJCAI 2013, pp. 1031–1038. AAAI Press/IJCAI (2013)Google Scholar
  24. 24.
    Marek, V.W., Nerode, A., Remmel, J.B.: How complicated is the set of stable models of a recursive logic program? Ann. Pure Appl. Logic 56(1–3), 119–135 (1992)MathSciNetCrossRefGoogle Scholar
  25. 25.
    Muller, D.E., Schupp, P.E.: Simulating alternating tree automata by nondeterministic automata: New results and new proofs of the theorems of rabin, mcnaughton and safra. Theor. Comput. Sci. 141(1&2), 69–107 (1995)MathSciNetCrossRefGoogle Scholar
  26. 26.
    Pearce, D.: A new logical characterisation of stable models and answer sets. In: Dix, J., Przymusinski, T.C., Moniz Pereira, L. (eds.) NMELP 1996. LNCS, vol. 1216, pp. 57–70. Springer, Heidelberg (1997) CrossRefGoogle Scholar
  27. 27.
    Šimkus, M.: Nonmonotonic Logic Programs with Function Symbols. Ph.D. thesis, Vienna University of Technology (2010)Google Scholar
  28. 28.
    Syrjänen, T.: Omega-restricted logic programs. In: Eiter, T., Faber, W., Truszczyński, M. (eds.) LPNMR 2001. LNCS (LNAI), vol. 2173, pp. 267–279. Springer, Heidelberg (2001) Google Scholar
  29. 29.
    Vardi, M.Y.: Reasoning about the past with two-way automata. In: Larsen, K.G., Skyum, S., Winskel, G. (eds.) ICALP 1998. LNCS, vol. 1443, pp. 628–641. Springer, Heidelberg (1998) CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Institute of Information SystemsTU WienViennaAustria

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