Abstract
An autoepistemic logic programming language is derived from a subset of a three-valued autoepistemic logic, called 3AEL. Autoepistemic programs generalize several ideas underlying logic programming: stable, supported, and well-founded models, Fitting's semantics, Kunen's semantics, and abductive frameworks can all be captured through simple autoepistemic translations; moreover, SLDNF-resolution and a generate-and-test method for stable semantics are generalized to provide sound and complete proof methods for autoepistemic programs. These methods extend existing proof methods for 3AEL. Thus autoepistemic logic programming, besides contributing to the understanding of 3AEL, can be seen as a unifying framework for the theory of logic programs. It should also be regarded as a first step toward a flexible environment where different forms of inference can be formally integrated.
Similar content being viewed by others
References
Apt, K.R., Blair, H. A. and Walker, A.: Towards a theory of declarative knowledge, in J. Minker (ed.),Foundations of Deductive Databases and Logic Programming, Kaufmann, Los Altos, 1988, pp. 89–148.
Baral, C. and Subrahmanian, V. S.: Stable and extension class theory for logic programs and default logic. Technical report CS-TR-2402, Dept. of Computer Science, University of Maryland, February 1990.Journal of Automated Reasoning (to appear).
Baral, C. and Subrahmanian, V. S.: Dualities between alternative semantics for logic programming and nonmonotonic reasoning, inProc. First Int. Workshop on Logic Programming and Non-monotonic Reasoning, pp. 69–86. MIT Press, 1991.
Bell, C., Nerode, A., Ng R. and Subrahmanian, V.S.: Implementing stable semantics by linear programming, inProc. of the International Workshop on Logic Programming and Nonmonotonic Reasoning (LP-NMR'93), MIT Press, Cambridge, 1993, pp. 23–42.
Bonatti, P.: A more general solution to the multiple expansion problem, inProc. of the Workshop on Non-Monotonic Reasoning and Logic Programming, NACLP'90.
Bonatti, P. A.: A family of three valued autoepistemic logics, in E. Ardizzone, S. Gaglio, and F. Sorbello (ed.),Trends in Artificial Intelligence: 2nd congress of the Italian Association for Artificial Intelligence — AI*IA. Lecture Notes in Artificial Intelligence 549. Springer-Verlag, Berlin, 1991, pp. 28–37.
Bonatti, P. A.: Autoepistemic logics as a unifying framework for the semantics of logic programs, in K. Apt (ed.),Proc. Joint International Conference and Symposium on Logic Programming (JIC-SLP'92), 1992.Journal of Logic Programming (to appear).
Bonatti, P. A.: Autoepistemic logic programming, inProc. of the International Workshop on Logic Programming and Nonmonotonic Reasoning (LPNMR'93), MIT Press, Cambridge, 1993, pp. 151–170.
Bonatti, P. A.: Three-valued beliefs and provability, and the semantics of logic programs, Ph.D. thesis TD-15/93, Universita di Pisa, March 1993.
Bondarenko, A., Toni, F. and Kowalski, R. A.: An assumption-based framework for non-monotonic reasoning, inProc International Workshop on Logic Programming and Nonmonotonic Reasoning (LPNMR'93), MIT Press, Cambridge, 1993, pp. 171–189.
Chan, D.: Constructive negation based on the completed database, in R. A. Kowalski and K. A. Bowen (ed.),Proc. of the Fifth Int. Cong. on Logic Programming, Seattle, 1988.
Chan, D.: An extension of constructive negation and its application in coroutining, in E. Lusk and R. Overbeek (eds.),Proc. North American Conf. on Logic Programming'89, MIT Press, Cambridge, Mass., 1989, pp. 477–493.
Clark, K. L.: Negation as failure, in Gallaire and Minker (ed.),Logic and Databases, Plenum Press, New York, 1978, pp. 293–322.
Di Pierro, A., Martelli, M. and Palamidessi, C.: Negation as instantiation: A new rule for the treatment of negation in logic programming, in K. Furukawa (ed.),Proc. 8th Int. Conf. on Logic Programming, MIT Press, Cambridge, Mass., 1991.
Davey, B. A. and Priestley, H. A.:Introduction to Lattices and Order. Cambridge University Press, 1990.
Dung, P. M.: Negation as hypothesis: An abductive foundation for logic programming, inProc. 8th Int. Conf. on Logic Programming, 1991.
Eshghi, K. and Kowalski, R. A.: Abduction compared with negation as failure, inProc. 6th Int. Conf. on Logic Programming, MIT Press, 1989.
Fitting, M.: A Kripke-Kleene semantics for general logic programs,J. Logic Programming 24(4) (1985).
Gelfond, M.: On stratified autoepistemic theories, inProc. AAAI-87, 1987, pp. 207–211.
Gelfond, M. and Lifschitz, V.: The stable model semantics for logic programming, inProc. 5th Int. Conf. and Symp. on Logic Programming, Seattle, Washington, 1988.
Kakas, A. C. and Mancarella, P.: Generalized stable models: A semantics for abduction, inProc. 9th European Conf. on Artificial Intelligence, Stockholm, Sweden, 1990.
Kunen, K.: Negation in logic programming,J. Logic Programming 4(4) (1987).
Kuo, K.: Programming in autoepistemic logic. Ph.D. thesis, State University of New York at Stony Brook, May 1992.
Lloyd, J. W.:Foundations of Logic Programming, Springer-Verlag, New York, 1984.
Marek, W. and Truszczynski, M.: Computing Intersection of autoepistemic expansions, inProc. 1st Int. Workshop on Logic Programming and Non-monotonic Reasoning, MIT Press, Cambridge, Mass, 1991, pp. 37–50.
Marek, W. and Subrahmanian, V. S.: The relationship between stable, supported, default and autoepistemic semantics for general logic programs,Theoret. Comput. Sci. 103 (1992) 365–386.
Moore, R.: Semantical considerations on nonmonotonic logics,Artificial Intelligence 25 (1985), 75–94.
Przymusinski, T.: Extended stable semantics for normal and disjunctive programs, inProc. 7th Int. Conf. on Logic Programming, 1990.
Przymusinski, T.: Autoepistemic logics of closed beliefs and logic programming, inProc. 1st Int. Workshop on Logic Programming and Non-monotonic Reasoning, MIT Press, 1991, pp. 3–20.
Schlipf, J. S.: The expressive power of the logic programming semantics, inProc. 9th ACM Symp. on Principles of Database Systems, ACM Press, 1990, pp. 196–204.
Truszczynski, M.: Embedding default logic into modal non-monotonic logic, inProc. 1st Int. Workshop on Logic Programming and Non-monotonic Reasoning, MIT Press, 1991, pp. 151–165.
Van Gelder, A., Ross, K. and Schlipf, J. S.: The well-founded semantics for general logic programs,Journal of the ACM 38(3) (1991), 620–650.
Author information
Authors and Affiliations
Additional information
This paper is an extended version of [8]. I am grateful to my advisor, Giorgio Levi, to Paolo Mancarella, who read the first version of the paper, and to the anonymous referees, whose comments led to sensible improvements.
Rights and permissions
About this article
Cite this article
Bonatti, P.A. Autoepistemic logic programming. J Autom Reasoning 13, 35–67 (1994). https://doi.org/10.1007/BF00881911
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF00881911