Abstract
In answer set programming, an extended logic program may have no answer set, or only one trivial answer set. In this paper, we propose a new stable model semantics based on the restricted four-valued logic to overcome both inconsistences and incoherences in answer set programming. Our stable models coincide with classical answer sets when reasoning on consistent and coherent logic programs, and can be solved by transformation in existing ASP solvers. We also show the connection between our stable models and the extensions of default logic.
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References
Alcântara, J., Damásio, C.V., Pereira, L.M.: A declarative characterisation of disjunctive paraconsistent answer sets. In: ECAI, vol. 16, p. 951. Citeseer (2004)
Amendola, G., Eiter, T., Leone, N.: Modular paracoherent answersets. In: Proceedings of Logics in Artificial Intelligence - 14th European Conference, JELIA 2014, Funchal, Madeira, Portugal, 24–26 September 2014, pp. 457–471 (2014). http://dx.doi.org/10.1007/978-3-319-11558-0_32
Arieli, O., Avron, A.: The value of the four values. Artif. Intell. 102(1), 97–141 (1998)
Belnap, N.: How a computer should think. In: Ryle, G. (ed.) Contemporary Aspects of Philosophy. Oriel Press Ltd., London (1977)
Belnap Jr., N.D.: A useful four-valued logic. In: Michael Dunn, J., Epstein, G. (eds.) Modern Uses of Multiple-valued Logic, pp. 5–37. Springer, Netherlands (1977)
Blair, H.A., Subrahmanian, V.: Paraconsistent logic programming. Theor. Comput. Sci. 68(2), 135–154 (1989)
Buccafurri, F., Leone, N., Rullo, P.: Enhancing disjunctive datalog by constraints. IEEE Trans. Knowl. Data Eng. 12(5), 845–860 (2000)
Chen, C., Lin, Z.: Restricted four-valued logic for default reasoning. Knowledge Science, Engineering and Management. LNCS, vol. 9403, pp. 40–52. Springer International Publishing, Cham (2015). http://dx.doi.org/10.1007/978-3-319-25159-2_4
Eiter, T., Fink, M., Moura, J.: Paracoherent answer set programming. In: KR, pp. 486–496 (2010)
Fitting, M.: Bilattices and the semantics of logic programming. J. Logic Program. 11(2), 91–116 (1991)
Fitting, M.: Fixpoint semantics for logic programming a survey. Theor. Comput. Sci. 278(1), 25–51 (2002)
Gelfond, M., Lifschitz, V.: Classical negation in logic programs and disjunctive databases. New Gener. Comput. 9(3–4), 365–385 (1991)
Leone, N., Pfeifer, G., Faber, W., Eiter, T., Gottlob, G., Perri, S., Scarcello, F.: The DLV system for knowledge representation and reasoning. ACM Trans. Comput. Logic (TOCL) 7(3), 499–562 (2006)
Odintsov, S., Pearce, D.J.: Routley semantics for answer sets. In: Baral, C., Greco, G., Leone, N., Terracina, G. (eds.) LPNMR 2005. LNCS (LNAI), vol. 3662, pp. 343–355. Springer, Heidelberg (2005)
Pearce, D.J., Valverde, A.: Quantified equilibrium logic and foundations for answer set programs. In: Garcia de la Banda, M., Pontelli, E. (eds.) ICLP 2008. LNCS, vol. 5366, pp. 546–560. Springer, Heidelberg (2008)
Reiter, R.: A logic for default reasoning. Artif. Intell. 13(1), 81–132 (1980)
Ruet, P., Fages, F.: Combining explicit negation and negation by failure via belnap’s logic. Theor. Comput. Sci. 171(1), 61–75 (1997)
Sakama, C., Inoue, K.: Paraconsistent stable semantics for extended disjunctive programs. J. Logic Comput. 5(3), 265–285 (1995)
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This work is partially supported by the Advance Programs Fund of Ministry of Education of China and Natural Science Foundation of China.
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Chen, C., Lin, Z. (2016). Restricted Four-Valued Semantics for Answer Set Programming. In: Booth, R., Zhang, ML. (eds) PRICAI 2016: Trends in Artificial Intelligence. PRICAI 2016. Lecture Notes in Computer Science(), vol 9810. Springer, Cham. https://doi.org/10.1007/978-3-319-42911-3_6
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DOI: https://doi.org/10.1007/978-3-319-42911-3_6
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