Abstract
We investigate the epistemological properties of MKNF, Lifschitz's logic of minimal knowledge and negation as failure. In particular, we show that the expressive power of MKNF is equivalent to Moore's autoepistemic logic (AEL), by defining an embedding of MKNF into AEL and vice versa. We also prove that the negation as failure modality not of MKNF exactly corresponds to the negative introspection operator in AEL. The two previous results imply that MKNF's minimal knowledge modality K can be represented by means of negation as failure not, i.e. MKNF theories admit an equivalent representation in terms of unimodal theories using the not operator only. This in turn implies that negation as failure is “more expressive” than minimal knowledge.
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References
A. Beringer and T. Schaub, 1993. Minimal belief and negation as failure: a feasible approach. In Proc. of AAAI-93, 400–405.
A. Bochman, 1995. On bimodal nonmonotonic modal logics and their unimodal and nonmodal equivalents. In Proc. of IJCAI-95, 1518–1524.
Y. Chen, 1994. The logic of only knowing as a unified framework for non-monotonic reasoning. Fundamenta Informaticae, 21, 205–220.
F. M. Donini, D. Nardi, and R. Rosati, 1997. Ground nonmonotonic modal logics. Journal of Logic and Computation, 7(4). To appear.
F. M. Donini, D. Nardi, and R. Rosati, 1997b. Autoepistemic description logics. To appear in Proc. of IJCAI-97.
M. Gelfond and V. Lifschitz. The stable model semantics for logic programming. In Logic Programming: Proc. of the fifth International Conference and Symposium, 1070–1080, 1988.
M. Gelfond, V. Lifschitz, H. Przymusinska, and M. Truszczyński, 1991. Disjunctive defaults. In Proc. of KR-91, 230–237.
G. Gottlob. Translating default logic into standard autoepistemic logic. Journal of ACM, 42:4:711–740, 1995.
J. Y. Halpern and Y. Moses. Towards a theory of knowledge and ignorance: Preliminary report. Technical Report CD-TR 92/34, IBM, 1985.
G. E. Hughes and M. J. Cresswell. An introduction to modal logic. Methuen, London, 1968.
K. Inoue and C. Sakama. On positive occurrences of negation as failure. In Proc. of KR-94, pages 293–304. Morgan Kaufmann, Los Altos, 1994.
V. Lifschitz, 1991. Nonmonotonic databases and epistemic queries. In Proc. of IJCAI-91, 381–386, Sydney.
V. Lifschitz, 1994. Minimal belief and negation as failure. AI Journal, 70:53–72.
V. Lifschitz and G. Schwarz, 1993. Extended logic programs as autoepistemic theories. In Proc. of LPNMR-93, 101–114, MIT Press.
V. Lifschitz and T. Woo, 1992. Answer sets in general nonmonotonic reasoning (preliminary report). In Proc. of KR-92, 603–614, Morgan Kaufmann.
F. Lin and Y. Shoham, 1992. Epistemic semantics for fixedpoint non-monotonic logics. AI Journal, 57:271–289.
W. Marek and M. Truszczyński, 1993. Nonmonotonic Logic — Context-Dependent Reasoning. Springer-Verlag.
R. C. Moore, 1985. Semantical considerations on nonmonotonic logic. AI Journal, 25:75–94.
R. Rosati, 1996. Minimal knowledge states in nonmonotonic modal logics. Proceedings of the Second Conference on Advances in Modal Logic (AiML96), CSLI, Stanford, USA.
R. Rosati, 1997. Reasoning with minimal belief and negation as failure: algorithms and complexity. To appear in Proceedings of AAAI-97.
G. Schwarz, 1992. Minimal model semantics for nonmonotonic modal logics. In Proceedings of the Seventh International Conference of Logic in Computer Science (LICS-92), pages 34–43. IEEE Computer Society Press, 1992.
G. Schwarz and M. Truszczyński, 1994. Minimal knowledge problem: a new approach. AI Journal, 67:113–141.
G. Schwarz. On embedding default logic into Moore's Autoepistemic Logic. AI Journal, 80:349:359, 1996.
Y. Shoham. Nonmonotonic logics: Meaning and utility. In Proc. of IJCAI-87, pp. 388–392, 1987.
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Rosati, R. (1997). Embedding minimal knowledge into autoepistemic logic. In: Lenzerini, M. (eds) AI*IA 97: Advances in Artificial Intelligence. AI*IA 1997. Lecture Notes in Computer Science, vol 1321. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63576-9_111
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DOI: https://doi.org/10.1007/3-540-63576-9_111
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