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Module theorem for the general theory of stable models. (English) Zbl 1261.68037

Summary: The module theorem by T. Janhunen et al. [J. Artif. Intell. Res. (JAIR) 35, 813–857 (2009; Zbl 1192.68129)] demonstrates how to provide a modular structure in answer set programming, where each module has a well-defined input/output interface which can be used to establish the compositionality of answer sets. The theorem is useful in the analysis of answer set programs, and is a basis of incremental grounding and reactive answer set programming.
We extend the module theorem to the general theory of stable models by P. Ferraris et al. [Artif. Intell. 175, No. 1, 236–263 (2011; Zbl 1227.68103)]. The generalization applies to non-ground logic programs allowing useful constructs in answer set programming, such as choice rules, the count aggregate, and nested expressions. Our extension is based on relating the module theorem to the symmetric splitting theorem by P. Ferraris et al. [“Symmetric splitting in the general theory of stable models”, in: Proceedings of the international joint conference on artificial intelligence (ICAI). 797–803 (2009)]. Based on this result, we reformulate and extend the theory of incremental answer set computation to a more general class of programs.

MSC:

68N17 Logic programming
68T27 Logic in artificial intelligence

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References:

[1] Lee, Proceedings of the AAAI Conference on Artificial Intelligence (AAAI) pp 472– (2008)
[2] Janhunen, Journal of Artificial Intelligence Research 35 pp 813– (2009)
[3] Gelfond, Proceedings of International Logic Programming Conference and Symposium pp 1070– (1988)
[4] Gebser, Proceedings of the Twenty-fourth International Conference on Logic Programming (ICLP’08) pp 190– (2008)
[5] DOI: 10.1007/978-3-642-20895-9_7 · Zbl 1327.68063 · doi:10.1007/978-3-642-20895-9_7
[6] Lee, Journal of Artificial Inteligence Research (JAIR) 43 pp 571– (2012)
[7] DOI: 10.1016/j.artint.2010.04.011 · Zbl 1227.68103 · doi:10.1016/j.artint.2010.04.011
[8] Ferraris, Proceedings of International Joint Conference on Artificial Intelligence (IJCAI) pp 372– (2007)
[9] Oikarinen, TPLP 8 pp 717– (2008)
[10] Lifschitz, Handbook of Logic in AI and Logic Programming pp 298– (1994)
[11] Ferraris, Proceedings of International Joint Conference on Artificial Intelligence (IJCAI) pp 797– (2009)
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