Abstract
Integrating diverse formalisms into modular knowledge representation systems offers increased expressivity, modeling convenience and computational benefits. We introduce the concepts of abstract inference modules and abstract modular inference systems to study general principles behind the design and analysis of model-generating programs, or solvers, for integrated multi-logic systems. We show how modules and modular systems give rise to transition graphs, which are a natural and convenient representation of solvers, an idea pioneered by the SAT community. We illustrate our approach by showing how it applies to answer-set programming and propositional logic, and to multi-logic systems based on these two formalisms.
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Bairakdar, S.E.-D., Dao-Tran, M., Eiter, T., Fink, M., Krennwallner, T.: The DMCS solver for distributed nonmonotonic multi-context systems. In: Janhunen, T., Niemelä, I. (eds.) JELIA 2010. LNCS, vol. 6341, pp. 352–355. Springer, Heidelberg (2010)
Barrett, C., Sebastiani, R., Seshia, S., Tinelli, C.: Satisfiability modulo theories. In: Biere, A., Heule, M., van Maaren, H., Walsch, T. (eds.) Handbook of Satisfiability, pp. 737–797. IOS Press (2008)
Brewka, G., Eiter, T.: Equilibria in heterogeneous nonmonotonic multi-context systems. In: Proceedings of National Conference on Artificial Intelligence (AAAI), pp. 385–390 (2007)
Denecker, M., Lierler, Y., Truszczynski, M., Vennekens, J.: A Tarskian informal semantics for answer set programming. In: Dovier, A., Costa, V.S. (eds.) International Conference on Logic Programming (ICLP). LIPIcs, vol. 17. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik (2012)
Eiter, T., Ianni, G., Schindlauer, R., Tompits, H.: A uniform integration of higher-order reasoning and external evaluations in answer set programming. In: Proceedings of International Joint Conference on Artificial Intelligence (IJCAI), pp. 90–96. Professional Book Center (2005)
Gebser, M., Kaufmann, B., Neumann, A., Schaub, T.: Conflict-driven answer set solving. In: Proceedings of 20th International Joint Conference on Artificial Intelligence (IJCAI 2007), pp. 386–392. MIT Press, Cambridge (2007)
Gebser, M., Schaub, T.: Tableau calculi for answer set programming. In: Etalle, S., Truszczyński, M. (eds.) ICLP 2006. LNCS, vol. 4079, pp. 11–25. Springer, Heidelberg (2006)
Gelfond, M., Lifschitz, V.: The stable model semantics for logic programming. In: Kowalski, R., Bowen, K. (eds.) Proceedings of International Logic Programming Conference and Symposium, pp. 1070–1080. MIT Press (1988)
Giunchiglia, E., Lierler, Y., Maratea, M.: Answer set programming based on propositional satisfiability. Journal of Automated Reasoning 36, 345–377 (2006)
Jaffar, J., Maher, M.: Constraint logic programming: A survey. Journal of Logic Programming 19(20), 503–581 (1994)
Järvisalo, M., Oikarinen, E., Janhunen, T., Niemelä, I.: A module-based framework for multi-language constraint modeling. In: Erdem, E., Lin, F., Schaub, T. (eds.) LPNMR 2009. LNCS, vol. 5753, pp. 155–168. Springer, Heidelberg (2009), http://dx.doi.org/10.1007/978-3-642-04238-6_15
Lierler, Y.: Abstract answer set solvers with backjumping and learning. Theory and Practice of Logic Programming 11, 135–169 (2011)
Lierler, Y.: On the relation of constraint answer set programming languages and algorithms. In: Proceedings of the AAAI Conference on Artificial Intelligence. MIT Press (2012)
Lierler, Y., Truszczynski, M.: Transition systems for model generators — a unifying approach. In: Theory and Practice of Logic Programming, 27th Int’l. Conference on Logic Programming (ICLP 2011), Special Issue 11(4-5) (2011)
Lierler, Y., Truszczynski, M.: Modular answer set solving. In: Proceedings of Twenty-Seventh AAAI Conference on Artificial Intelligence (AAAI 2013) (2013)
Marek, V., Truszczyński, M.: Stable models and an alternative logic programming paradigm. In: The Logic Programming Paradigm: a 25-Year Perspective, pp. 375–398. Springer (1999)
Mariën, M., Wittocx, J., Denecker, M., Bruynooghe, M.: SAT(ID): Satisfiability of propositional logic extended with inductive definitions. In: Kleine Büning, H., Zhao, X. (eds.) SAT 2008. LNCS, vol. 4996, pp. 211–224. Springer, Heidelberg (2008)
Niemelä, I.: Logic programs with stable model semantics as a constraint programming paradigm. Annals of Mathematics and Artificial Intelligence 25, 241–273 (1999)
Niemelä, I., Simons, P.: Extending the Smodels system with cardinality and weight constraints. In: Minker, J. (ed.) Logic-Based Artificial Intelligence, pp. 491–521. Kluwer (2000)
Nieuwenhuis, R., Oliveras, A., Tinelli, C.: Solving SAT and SAT modulo theories: From an abstract Davis-Putnam-Logemann-Loveland procedure to DPLL(T). Journal of the ACM 53(6), 937–977 (2006)
Oikarinen, E., Janhunen, T.: Modular equivalence for normal logic programs. In: 17th European Conference on Artificial Intelligence (ECAI), pp. 412–416 (2006)
Rossi, F., van Beek, P., Walsh, T.: Constraint programming. In: van Harmelen, F., Lifschitz, V., Porter, B. (eds.) Handbook of Knowledge Representation, pp. 181–212. Elsevier (2008)
Tasharrofi, S., Ternovska, E.: A semantic account for modularity in multi-language modelling of search problems. In: Tinelli, C., Sofronie-Stokkermans, V. (eds.) FroCoS 2011. LNCS, vol. 6989, pp. 259–274. Springer, Heidelberg (2011)
Tasharrofi, S., Wu, X.N., Ternovska, E.: Solving modular model expansion tasks. CoRR abs/1109.0583 (2011)
Van Gelder, A., Ross, K., Schlipf, J.: The well-founded semantics for general logic programs. Journal of ACM 38(3), 620–650 (1991)
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Lierler, Y., Truszczynski, M. (2014). Abstract Modular Inference Systems and Solvers. In: Flatt, M., Guo, HF. (eds) Practical Aspects of Declarative Languages. PADL 2014. Lecture Notes in Computer Science, vol 8324. Springer, Cham. https://doi.org/10.1007/978-3-319-04132-2_4
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DOI: https://doi.org/10.1007/978-3-319-04132-2_4
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