Skip to main content Accessibility help

Disjunctive logic programs with existential quantification in rule heads

  • JIA-HUAI YOU (a1), HENG ZHANG (a2) and YAN ZHANG (a2)


We consider disjunctive logic programs without function symbols but with existential quantification in rule heads, under the semantics of general stable models. There are at least two interesting prospects in these programs. The first is that a program can be made more succinct by using existential variables, and the second is on the potential in representing defeasible ontological knowledge by these logic programs. This paper studies some of the properties of these programs. First, we show a simple yet intuitive definition of stable models for these programs that does not resort to second-order logic. Second, the stable models of these programs can be characterized by an extension of progression for disjunctive programs, which provides a native characterization of justification for stable models. We then study the decidability issue. While the stable model existence problem for safe disjunctive programs is decidable, with existential quantification allowed in rule heads the problem becomes undecidable. We identify an interesting decidable fragment by exploring a new notion of stratification over existential quantification.



Hide All
Alviano, M., Faber, W., Leone, N. and Manna, M. 2012. Disjunctive datalog with existential quantifiers: Semantics, decidability, and complexity issues. Theory and Practice of Logic Programming 12, 4–5, 701718.
Bartholomew, M. and Lee, J. 2010. A decidable class of groundable formulas in the general theory of stable models. In Proc. KR-2010.
Berger, R. 1966. The undecidability of the domino problem. Memoirs of the American Mathematical Society 66, 1, 172.
Bonatti, P. A., Faella, M. and Sauro, L. 2011. Defeasible inclusions in low-complexity DLs. Journal of Artificial Intelligence Research 42, 719764.
Cabalar, P., Pearce, D. and Valverde, A. 2009. A revised concept of safety for general answer set programs. In Proc. LPNMR, 58–70.
Cadoli, M., Eiter, T. and Gottlob, G. 1997. Default logic as a query language. IEEE Transactions on Knowledge and Data Engineering 9, 3, 448463.
Calì, A., Gottlob, G. and Kifer, M. 2008. Taming the infinite chase: Query answering under expressive relational constraints. In KR, 70–80.
Calì, A., Gottlob, G. and Lukasiewicz, T. 2009. A general datalog-based framework for tractable query answering over ontologies. In Proc. PODS, 77–86.
Calì, A., Gottlob, G. and Pieris, A. 2012. Towards more expressive ontology languages: The query answering problem. Artificial Intelligence 193, 87128.
Casini, G. and Straccia, U. 2011. Defeasible inheritance-based description logics. In Proc. IJCAI-11, 813–818.
Eiter, T., Gottlob, G. and Mannila, H. 1997. Disjunctive datalog. ACM Transactions Database System 22, 3, 364418.
Fages, F. 1994. Consistency of clark's completion and existence of stable models. Journal of Methods of Logic in Computer Science 1, 5160.
Fagin, R., Kolaitis, P. G., Miller, R. J. and Popa, L. 2005. Data exchange: Semantics and query answering. Theoretical Computer Science 336, 1, 89124.
Ferraris, P., Lee, J. and Lifschitz, V. 2011. Stable models and circumscription. Artificial Intelligence 175, 1, 236263.
Ferraris, P., Lee, J., Lifschitz, V. and Palla, R. 2009. Symmetric splitting in the general theory of stable models. In IJCAI-09, 797–803.
Gelfond, M. and Lifschitz, V. 1988. The stable model semantics for logic programming. In Proc. ICLP'88, 1070–1080.
Gottlob, G., Hernich, A., Kupke, C. and Lukasiewicz, T. 2012. Equality-friendly well-founded semantics and applications to description logics. In Proc. AAAI-12.
Gurevich, Y. and Koryakov, I. 1972. Remarks on Berger's paper on the domino problem. Siberian Mathematical Journal 13, 319321.
Lee, J., Lifschitz, V. and Palla, R. 2008. Safe formulas in the general theory of stable models (preliminary report). In Proc. ICLP, 672–676.
Lee, J. and Meng, Y. 2011. First-order stable model semantics and first-order loop formulas. Journal of Artificial Intelligence Research (JAIR) 42, 125180.
Lee, J. and Palla, R. 2012. Reformulating the situation calculus and the event calculus in the general theory of stable models and in answer set programming. Journal of Artificial Intelligence Research (JAIR) 43, 571620.
Leone, N., Manna, M., Terracina, G. and Veltri, P. 2012. Efficiently computable datalog; programs. In KR.
Leone, N., Pfeifer, G., Faber, W., Eiter, T., Gottlob, G., Perri, S. and Scarcello, F. 2006. The DLV system for knowledge representation and reasoning. ACM Transactions on Computational Logic 7, 3, 499562.
Lin, F. and Zhou, Y. 2011. From answer set logic programming to circumscription via logic of GK. Artificial Intelligence 175, 1, 264277.
Motik, B. and Rosati, R. 2010. Reconciling description logics and rules. Journal of the ACM 57, 5, 162.
Niemelä, I. 1999. Logic programs with stable model semantics as a constraint programming paradigm. Annals of Mathematics and Artificial Intelligence 25, 3–4, 241273.
Nieuwenhuis, R., Oliveras, A. and Tinelli, C. 2006. Solving SAT and SAT modulo theories: From an abstract davis–putnam–logemann–loveland procedure to DPLL(T). Journal of ACM 53, 6, 937977.
You, J.-H., Shen, Y.-D. and Wang, K. 2012. Well-supported semantics for logic programs with generalized rules. In Correct Reasoning: Essays on Logic-Based AI in Honor of Vladimir Lifschitz, LNCS 7265, 576–591.
Zhang, H. and Ying, M. 2010. Decidable fragments of first-order language under stable model semantics and circumscription. In Proc. AAAI-10.
Zhang, H., Zhang, Y., Ying, M. and Zhou, Y. 2011. Translating first-order theories into logic programs. In Proc. IJCAI-11, 1126–1131.
Zhou, Y. and Zhang, Y. 2011. Progression semantics for disjunctive logic programs. In Proc. AAAI-11, 286–291.


Type Description Title
Supplementary materials

You et al. supplementary material

 PDF (194 KB)
194 KB

Disjunctive logic programs with existential quantification in rule heads

  • JIA-HUAI YOU (a1), HENG ZHANG (a2) and YAN ZHANG (a2)


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed