Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-23T11:39:31.820Z Has data issue: false hasContentIssue false
  • English
  • Français

Inconsistency Proofs for ASP: The ASP - DRUPE Format

Published online by Cambridge University Press:  20 September 2019

MARIO ALVIANO Open the ORCID record for MARIO ALVIANO [Opens in a new window] ,
CARMINE DODARO Open the ORCID record for CARMINE DODARO [Opens in a new window] ,
JOHANNES K. FICHTE ,
MARKUS HECHER Open the ORCID record for MARKUS HECHER [Opens in a new window] ,
TOBIAS PHILIPP  and
JAKOB RATH
MARIO ALVIANO
Affiliation:
University of Calabria, Italy (e-mail: [email protected])
CARMINE DODARO
Affiliation:
University of Calabria, Italy (e-mail: [email protected])
JOHANNES K. FICHTE
Affiliation:
TU Dresden, Germany (e-mail: [email protected])
MARKUS HECHER
Affiliation:
TU Wien, Austria (e-mail: [email protected])
TOBIAS PHILIPP
Affiliation:
secunet Security Networks AG, Germany (e-mail: [email protected])
JAKOB RATH
Affiliation:
TU Wien, Austria (e-mail: [email protected])
Get access Rights & Permissions [Opens in a new window]

Abstract

Answer Set Programming (ASP) solvers are highly-tuned and complex procedures that implicitly solve the consistency problem, i.e., deciding whether a logic program admits an answer set. Verifying whether a claimed answer set is formally a correct answer set of the program can be decided in polynomial time for (normal) programs. However, it is far from immediate to verify whether a program that is claimed to be inconsistent, indeed does not admit any answer sets. In this paper, we address this problem and develop the new proof format ASP-DRUPE for propositional, disjunctive logic programs, including weight and choice rules. ASP-DRUPE is based on the Reverse Unit Propagation (RUP) format designed for Boolean satisfiability. We establish correctness of ASP-DRUPE and discuss how to integrate it into modern ASP solvers. Later, we provide an implementation of ASP-DRUPE into the wasp solver for normal logic programs.

Keywords

Answer Set ProgrammingReverse Unit Propagation proofsinconsistency proofs
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. 891 - 907
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

Alviano, M., Dodaro, C., Leone, N., and Ricca, F. 2015. Advances in WASP. In LPNMR 2015. LNCS, vol. 9345. Springer, 40–54.Google Scholar
Alviano, M., Dodaro, C., and Maratea, M. 2018. Shared aggregate sets in answer set programming. TPLP 18, 3-4, 301–318.Google Scholar
Balduccini, M., Gelfond, M., and Nogueira, M. 2006. Answer set based design of knowledge systems. Ann. Math. Artif. Intell. 47, 1-2, 183–219.Google Scholar
Bomanson, J., Gebser, M., Janhunen, T., Kaufmann, B., and Schaub, T. 2016. Answer set programming modulo acyclicity. Fundam. Inform. 147, 1, 63–91.Google Scholar
Brewka, G., Eiter, T., and Truszczyński, M. 2011. Answer set programming at a glance. Communications of the ACM 54, 12, 92–103.CrossRefGoogle Scholar
Calimeri, F., Faber, W., Gebser, M., Ianni, G., Kaminski, R., Krennwallner, T., Leone, N., Ricca, F., and Schaub, T. 2015. ASP-core-2 input language format.Google Scholar
Clark, K. L. 1977. Negation as failure. In Symposium on Logic and Data Bases 1977. Advances in Data Base Theory. Plemum Press, 293–322.Google Scholar
Cruz-Filipe, L., Heule, M. J. H. , Jr., W. A. H., Kaufmann, M., and Schneider-Kamp, P. 2017. Efficient certified RAT verification. In CADE 2017. LNCS, vol. 10395. Springer, 220–236.Google Scholar
Eén, N. and Biere, A. 2005. Effective preprocessing in SAT through variable and clause elimination. In SAT 2005. LNCS, vol. 3569. Springer, 61–75.Google Scholar
Faber, W. 2005. Unfounded sets for disjunctive logic programs with arbitrary aggregates. In LPNMR 2005. LNCS, vol. 3662. Springer, 40–52.Google Scholar
Faber, W., Pfeifer, G., and Leone, N. 2011. Semantics and complexity of recursive aggregates in answer set programming. Artif. Intell. 175, 1, 278–298.CrossRefGoogle Scholar
Fages, F. 1994. Consistency of clark’s completion and existence of stable models. Meth. of Logic in CS 1, 1, 51–60.Google Scholar
Ferraris, P. 2011. Logic programs with propositional connectives and aggregates. ACM Trans. Comput. Log. 12, 4, 25:1–25:40.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 KR 2010. The AAAI Press, 497–507.Google Scholar
Gebser, M., Kaminski, R., Kaufmann, B., Ostrowski, M., Schaub, T., and Wanko, P. 2016. Theory solving made easy with clingo 5. In ICLP (Tech. C.). OASICS, vol. 52. Dagstuhl Pub., 2:1–2:15.Google Scholar
Gebser, M., Kaminski, R., Kaufmann, B., and Schaub, T. 2011. Multi-Criteria Optimization in Answer Set Programming. In ICLP 2011. LIPIcs, vol. 11. Dagstuhl Pub., 1–10.Google Scholar
Gebser, M., Kaminski, R., Kaufmann, B., and Schaub, T. 2012. Answer Set Solving in Practice . Synthesis Lectures on Artificial Intelligence and Machine Learning. Morgan & Claypool Publishers.Google Scholar
Gebser, M., Kaufmann, B., Neumann, A., and Schaub, T. 2008. Advanced preprocessing for answer set solving. In ECAI 2008. Frontiers in Artificial Intelligence and Applications, vol. 178. IOS Press, 15–19.Google Scholar
Gebser, M., Obermeier, P., Ratsch-Heitmann, M., Runge, M., and Schaub, T. 2018. Routing driverless transport vehicles in car assembly with answer set programming. CoRR abs/1804.10437.Google Scholar
Gebser, M., Schaub, T., Thiele, S., and Veber, P. 2011. Detecting inconsistencies in large biological networks with answer set programming. TPLP 11, 2-3, 323–360.Google Scholar
Gelder, A. V. 2008. Verifying RUP proofs of propositional unsatisfiability. In International Symposium on Artificial Intelligence and Mathematics, ISAIM 2008, Fort Lauderdale, Florida, USA, January 2-4, 2008.Google Scholar
Gelfond, M. and Zhang, Y. 2014. Vicious circle principle and logic programs with aggregates. TPLP 14, 4-5, 587–601.Google Scholar
Goldberg, E. I. and Novikov, Y. 2003. Verification of proofs of unsatisfiability for CNF formulas. In DATE. IEEE Computer Society, 10886–10891.Google Scholar
Guziolowski, C., Videla, S., Eduati, F., Thiele, S., Cokelaer, T., Siegel, A., and Saez-Rodriguez, J. 2013. Exhaustively characterizing feasible logic models of a signaling network using answer set programming. Bioinformatics 29, 18, 2320–2326. Erratum see Bioinformatics 30, 13, 1942.CrossRefGoogle Scholar
Haubelt, C., Neubauer, K., Schaub, T., and Wanko, P. 2018. Design space exploration with answer set programming. KI - Künstliche Intelligenz 32, 2, 205–206.CrossRefGoogle Scholar
Heule, M., Hunt, Jr. , W. A., and Wetzler, N. 2013. Verifying refutations with extended resolution. In CADE 2013. LNCS, vol. 7898. Springer, 345–359.Google Scholar
Heule, M., Hunt, Jr. , W. A., and Wetzler, N. 2015. Expressing symmetry breaking in DRAT proofs. In CADE 2015. LNCS, vol. 9195. Springer, 591–606.Google Scholar
Heule, M., Seidl, M., and Biere, A. 2014. A unified proof system for QBF preprocessing. In IJCAR. LNCS, vol. 8562. Springer, 91–106.Google Scholar
Janhunen, T. 2006. Some (in)translatability results for normal logic programs and propositional theories. Journal of Applied Non-Classical Logics 16, 1-2, 35–86.Google Scholar
Kiesl, B., Rebola-Pardo, A., and Heule, M. J. H. 2018. Extended resolution simulates DRAT. In IJCAR 2018. LNCS, vol. 10900. Springer, 516–531.Google Scholar
Lin, F. and Zhao, J. 2003. On tight logic programs and yet another translation from normal logic programs to propositional logic. In IJCAI’03. Morgan Kaufmann, 853–858.Google Scholar
Liu, L., Pontelli, E., Son, T. C., and Truszczynski, M. 2010. Logic programs with abstract constraint atoms: The role of computations. Artif. Intell. 174, 3-4, 295–315.CrossRefGoogle Scholar
Lonsing, F. and Egly, U. 2018. QRAT+: generalizing QRAT by a more powerful QBF redundancy property. In IJCAR. LNCS, vol. 10900. Springer, 161–177.Google Scholar
Pearce, D. 1999. Stable inference as intuitionistic validity. J. Log. Program. 38, 1, 79–91.CrossRefGoogle Scholar
Pelov, N., Denecker, M., and Bruynooghe, M. 2007. Well-founded and stable semantics of logic programs with aggregates. Theory and Practice of Logic Programming 7, 3, 301–353.Google Scholar
Philipp, T. and Rebola-Pardo, A. 2016. DRAT proofs for XOR reasoning. In JELIA 2016. LNCS, vol. 10021. Springer, 415–429.Google Scholar
Ricca, F., Grasso, G., Alviano, M., Manna, M., Lio, V., Iiritano, S., and Leone, N. 2012. Team-building with answer set programming in the Gioia-Tauro seaport. TPLP 12, 361–381.Google Scholar
Silva, J. P. M. and Sakallah, K. A. 1999. GRASP: A search algorithm for propositional satisfiability. IEEE Trans. Computers 48, 5, 506–521.CrossRefGoogle Scholar
Son, T. C. and Pontelli, E. 2007. A constructive semantic characterization of aggregates in answer set programming. Theory and Practice of Logic Programming 7, 3, 355–375.CrossRefGoogle Scholar
Syrjänen, T. 2000. Lparse 1.0 User’s Manual.Google Scholar
Truszczyński, M. 2011. Trichotomy and dichotomy results on the complexity of reasoning with disjunctive logic programs. TPLP 11, 881–904.Google Scholar
Wetzler, N., Heule, M., and Hunt, Jr. , W. A. 2014. DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In SAT 2014. LNCS, vol. 8561. Springer, 422–429.Google Scholar