An Overview of Nonmonotonic Reasoning and Logic Programming
Journal of Logic Programming, Vol. 17, No. 2, 3, \& 4, 95-126, Nov. 1993
- Department of Computer Science and
- Institute for Advanced Computer Studies
- University of Maryland, College Park, MD 20742
The complete paper is available in:
available.
Abstract
The focus of this paper is nonmonotonic reasoning as it relates to logic programming.
I discuss the pre-history of nonmonotonic reasoning starting from approximately 1958.
I then review the research that has been accomplished in the areas of circumscription,
default theory, modal theories and logic programming. The overview includes the major
results developed including complexity results that are known about the various theories.
I then provide a summary which includes an assessment of the field and what must be
done to further research in nonmonotonic reasoning and logic programming.
Bibliography
-
[AB88] K.R. Apt and H.A. Blair. Arithmetic classification of perfect models of stratified programs.
R.A. Conference and Symposium on Logic Programming, pages 766-779, 1988.
-
[AB90] K.R. Apt and M. Bezem Acyclic programs. Logic Programming: Proceedings of the Seventh
International Conference, D.H.D. Warren an P. Szeredi, eds. MIT Press, 617-633, 1990.
-
[ABW88] K.R. Apt, H.A. Blair, and A. Walker. Towards a theory of declarative knowledge. In
J. Minker, editor, Foundations of Deductive Databases and Logic Programming, pages
89-148. Morgan Kaufmann Pub., Washington, D.C., 1988.
-
[AP92] J.J. Alferes and L.M. Pereira. On logic program semantics with two kinds of negation. In
Proceedings of the Joint International Conference and Symposium on Logic Programming,
pages 574-588, 1992.
-
[BE89] A. Borgida and D.W. Etherington. Hierarchical knowledge bases and efficient disjunction.
In Proceedings of the First International Conference on Principle of Knowledge Represen-
tation and Reasoning (KR-89), pages 33-43, Toronto, Ontario, Canada, 1989.
-
[BF88] N. Bidoit and C. Froidevaux. General logical databases and programs: Default logic
semantics and stratification. Journal of Information and Computation, v.91, no.1, 15-54,
March, 1991.
-
[BH86] N. Bidoit and R. Hull. Positivism vs. minimalism in deductive databases. Proc. ACM
SIGACT-SIGMOD Symposium on the Principles of Database Systems, pages 123-132,
1986.
-
[BKMS91] C. Baral, S. Kraus, J. Minker, and V.S. Subrahmanian. Combining knowledge bases
consisting of first order theories. Computational Intelligence , 8(1), 45-71, March 1992.
-
[BLM90a] C. Baral, J. Lobo, and J. Minker. Generalized disjunctive well-founded semantics for
logic programs: Declarative semantics. In Proc. of Fifth International Symposium on
Methodologies for Intelligent Systems, 465-473, Knoxville, TN, 1990.
-
[BLM90b] C. Baral, J. Lobo, and J. Minker. Generalized disjunctive well-founded semantics for
logic programs: Procedural semantics. In Proc. of Fifth International Symposium on
Methodologies for Intelligent Systems, 456-464, Knoxville, TN, 1990.
-
[BLM90c] C. Baral, J. Lobo, and J. Minker. Generalized well-founded semantics for logic programs.
In M. E. Stickel, editor, Proc. of Tenth International Conference on Automated Deduction,
pages 102-116, Kaiserslautern, FRG, July, 1990. Springer-Verlag.
-
[BLM91] C. Baral, J. Lobo, and J. Minker. WF3: A semantics for negation in normal disjunctive
logic programs. In Proc. of sixth International Symposium on Methodologies for Intelligent
Systems, 459-468, Charlotte, NC, 1991.
-
[BNNS91] C. Bell, A. Nerode, R. Ng, and V.S. Subrahmanian. Computation and implementation
of non-monotonic deductive databases. Technical report, Dept. of Computer Science,
University of Maryland at College Park, 1991.
-
[BR92] L. Bertossi and R. Reiter. Circumscription and Generic Mathematical Objects. Technical
Report, University of Toronto, 1992.
-
[BS85] G. Bossu and P. Siegel. Saturation, nonmonotonic reasoning and the closed-world assump-
tion. Artificial Intelligence, 25(1):13-63, 1985 January 1985.
-
[BS89] H. Blair and V.S. Subrahmanian. Paraconsistent Logic Programming. Theoretical Com-
puter Science, 68:135-154, 1989.
-
[BS91] C. Baral and V. S. Subrahmanian. Dualities between alternative semantics of logic pro-
grams and nonmonotonic formalisms. In A. Nerode, W. Marek, and V.S. Subrahmanian,
editors, Logic Programming and Non-monotonic Reasoning: Proceedings of the First In-
ternational Workshop, pages 69-86. MIT Press, 1991.
-
[BS92] C. Baral and V.S. Subrahmanian. Stable and extension class theory for logic programs
and default logics. Journal of Automated Reasoning, 8:345-366, 1992.
-
[Bar91] C. Baral. Issues in Knowledge Representation: Semantics and Knowledge Combination.
PhD thesis, University of Maryland, College Park, Maryland 20742, 1991.
-
[Bar92] C. Baral. Generalized negation as failure and semantics of normal disjunctive logic pro-
grams. In International Conference on Logic Programming and Automated Reasoning:
Lecture Notes in AI 624, Springer Verlag, pages 309-319, 1992.
-
[Bel77a] N. Belnap. How a computer should think. In G. Ryle, editor, Contemporary Aspects of
Philosophy, pages 30-56. Oriel Press, 1977.
-
[Bel77b] N. Belnap. A useful four-valued logic. In J.M. Dunn and G. Epstein, editors, Modern Uses
of Multiple-valued Logic, pages 8-37. D. Reidel, 1977.
-
[Bid91] N. Bidoit. Negation in rule-based database languages: a survey. Theoretical Computer
Science, 78, 3-83, 1991.
-
[Bon92] P.A. Bonatti. Autoepistemic logics as a unifying framework for the semantics of logic
programs. In Proceedings of the Joint International Conference and Symposium on Logic
Programming, pages 417-430, 1992.
-
[Bre89] Ph. Bresnard. An Introduction to Default Logic. Springer-Verlag, 1989.
-
[Bre91] G. Brewka. Nonmonotonic Reasoning: Logical Foundations of Common Sense. Cambridge
University Press, Cambridge, 1991.
-
[CH82] A. Chandra and D. Harel. Structure and complexity of relational queries. Journal of
Computer System Sciences, 25:99-128, 1982.
-
[CKPR73] A. Colmerauer, H. Kanoui, R. Pasero, and P. Roussel. Un systeme de communication
homme-machine en francais. Technical report, Groupe de Intelligence Artificielle Univer-
sitae de Aix-Marseille II, Marseille, 1973.
-
[CL90] M. Cadoli and M. Lenzerini. The complexity of closed world reasoning and circumscription.
Proceedings of the AAAI, pages 550-555, 1990 Also Technical report, Universita di Roma
"La Sapienza", Dipartimento di Informatica e Sistemistica, Roma, Italy, 1990.
-
[CS89] J. Chomicki and V.S. Subrahmanian. Generalized closed world assumption is ss02 com-
plete. Technical Report TR-89-036, Computer Science Department, University of North
Carolina, 1989. Information Processing Letters., 34:289-291, 1990.
-
[CS92] M. Cadoli and M. Schaerf. A survey on complexity results for non-monotonic logics.
Technical report, Universita di Roma "La Sapienza", Dipartiment o di Informatica e Sis-
temistica, Roma, Italy, 1992.
-
[CW92] W. Chen and D.S. Warren. A goal oriented approach to computing well founded se-
mantics. In Proceedings of the Joint International Conference and Symposium on Logic
Programming, pages 589-606, 1992.
-
[Cha88] D. Chan. Constructive negation based on the completed databases. In R.A. Kowalski
and K.A. Bowen, editors, Proc. 5th International Conference and Symposium on Logic
Programming, pages 111-125, Seattle, Washington, August 15-19, 1988.
-
[Cla78] K.L. Clark. Negation as failure. In Logic and Databases, eds. H. Gallaire and J. Minker,
293-322, Plenum, New York, 1978.
-
[DD92] M. Denecker and D. De Schreye. Sldnfa: an abductive procedure for normal abductive
programs. In Proceedings of the Joint International Conference and Symposium on Logic
Programming, pages 686-702, 1992.
-
[DLNPS90] F.M. Donini, M. Lenzerini, D. Nardi, F. Pirri, M. Schaerf Nonmonotonic reasoning
Artificial Intelligence Review, vol. 4, 163-210, 1990.
-
[DeK86] J. de Kleer. An assumption-based TMS. Artificial Intelligence, 32, 1986.
-
[Del88] J. Delgrande. An approach to default reasoning based on a first-order conditional logic:
revised report. Artificial Intelligence, 36:63-90, 1988.
-
[Dem68] A.P. Dempster. A Generalization of Bayesian Inference. J. of the Royal Statistical Society,
Series B, 30, 205-247, 1968.
-
[Dix91] J. Dix. Classifying semantics of logic programs. In A. Nerode, W. Marek, and V.S.
Subrahmanian, editors, Logic Programming and Non-monotonic Reasoning: Proceedings
of the First International Workshop, pages 166-180. MIT Press, 1991.
-
[Dix92] J. Dix. Classifying semantics of disjunctive logic program. In Proceedings of the Joint
International Conference and Symposium on Logic Programming, pages 798-812, 1992.
-
[Doy79] J. Doyle. A truth maintenance system. Artificial Intelligence, 12:231-272, l979.
-
[Doy82] J. Doyle. Some theories of reasoned assumptions: An essay in rational psychology. Tech-
nical Report, Department of Computer Science, Carnegie-Mellon University, 1982.
-
[Doy83] J. Doyle. The ins and outs of reason maintenance. In Proceedings of Eighth IJCAI, pp.
349-351, 1983.
-
[Dung92] P.M. Dung. On the relations between stable and well-founded semantics of logic programs.
Theoretical Computer Science: Logic, semantics and theory of programming, 105:7-26,
1992.
-
[EDP90] J. Elgot-Drapkin and D. Perlis. Reasoning situated in time i: basic concepts. J. of
Experimental and Theoretical Artificial Intelligence, 2:75-98, 1990.
-
[EK76] M.H. van Emden and R.A. Kowalski The semantics of predicate logic as a programming
language Journal of the ACM, 23(4), pp. 733-742, 1976.
-
[EK88] K. Eshghi and R.A. Kowalski. Abduction through deduction. Technical Report, Dept. of
Computing, Imperial College, London, 1988.
-
[EK89] K. Eshghi and R.A. Kowalski. Abduction compared with negation by failure. In Proc. 6th
International Conference on Logic Programming, 234-255, Lisbon, 1989.
-
[EKP91] D. Etherington, S. Kraus, and D. Perlis. Nonmonotonicity and the scope of reasoning.
Artificial Intelligence, 52:221-261, 1991.
-
[EMR85] D. Etherington, R. Mercer, and R. Reiter. On the adequacy of predicate circumscription
for closed world reasoning. Computational Intelligence 1, pages 11-15, 1985.
-
[ER83] D.W. Etherington and R. Reiter. On inheritance hierarchies with exceptions. In Pro-
ceedings of American Association for Artificial Intelligence at National Conference, pages
104-108, 1983.
-
[Esh88] K. Eshghi. Abductive planning with event calculus. In Proc. 5th International Conference
and Symposium on Logic Programming, 562-579, Seattle, Washington, 1988.
-
[Esh90] K. Eshghi. Diagnoses as stable models. In Proc. 1st International Workshop on Principles
of Diagnoses, Menlo Park, CA, 1990.
-
[Eva89] C. Evans Negation-as-failure as an approach to the Hanks and McDermott problem.
Proceedings of the Second International Conference on Artificial Intelligence, 1969.
-
[FLM91] M. Freund, D. Lehmann and P. Morris. Rationality, transitivity and contraposition. Ar-
tificial Intelligence, 52, 191-203, 1991.
-
[FLMS93] J.A. Fernandez, J. Lobo, J. Minker, and V.S. Subrahmanian. Disjunctive LP + integrity
constraints = stable model semantics. In Annals of Mathematics and AI 8, No. 3-4 (1993)
-
[FM91a] J.A. Fernandez and J. Minker. Bottom-up evaluation of hierarchical disjunctive deductive
databases. In Proc. International Conference on Logic Programming, 660-675, Paris, 1991.
MIT Press.
-
[FM91b] J.A. Fernandez and J. Minker. Computing perfect models of disjunctive stratified
databases. In Proc. ILPS '91 Workshop on Disjunctive Logic Programs, 110-117, eds.
D. Loveland, J. Lobo, and A. Rajasekar, San Diego, CA, Oct. 1991.
-
[FM92a] J.A. Fernandez and J. Minker. Semantics of disjunctive deductive databases. In Interna-
tional Conference on Database Theory: Lecture Notes in Computer Science 646, Springer
Verlag, pages 21-50, 1992.
-
[FM92b] J.A. Fernandez and J. Minker. Disjunctive deductive databases. In International Confer-
ence on Logic Programming and Automated Reasoning: Lecture Notes in AI 624, Springer
Verlag, pages 332-356, 1992.
-
[FM93] J.A. Alberto Fern'andez and J. Minker. Theory and algorithms for disjunctive deductive
databases. Programmirovanie Journal, 1993. Invited Paper by the Academy of Sciences
of Russia (To appear).
-
[Fah79] S.E. Fahlman. Netl: A System for Representing and Using Real-World Knowledge. M.I.T.
Press, 1979.
-
[Fit85] M. Fitting. A Kripke-Kleene semantics for logic programs. Journal of Logic Programming,
2(4):295-312, 1985.
-
[Fit91] M.C. Fitting. Well-founded semantics, generalized. In International Symposium on Logic
Programming, pages 71-84, 1991.
-
[GL88] M. Gelfond and V. Lifschitz. The stable model semantics for logic programming. In
Proceedings of the 5th Logic Programming Symposium, pages 1070-1080, Association for
Logic Programming, MIT Press, Cambridge, Mass, 1988.
-
[GL90] M. Gelfond and V. Lifschitz Logic programs with classical negation. Logic Programming:
Proceedings of the Seventh International Conference, D.H.D. Warren and P. Szeredi, eds.,
579-597, 1990.
-
[GL91] M. Gelfond and V. Lifschitz. Classical negation in logic programming and disjunctive
databases. New Generation Computing, 9:365-385, 1991.
-
[GL92] M. Gelfond and V. Lifschitz. Representing actions in extended logic programming. In
Proceedings of the Joint International Conference and Symposium on Logic Programming,
pages 559-573, 1992.
-
[GLPT91] M. Gelfond, V. Lifschitz, H. Przymusi'nska, and M. Truszczy'nski. Disjunctive defaults.
In J. Allen, R. Fikes, and E. Sandewall, editors, Principles of Knowledge Representation
and Reasoning: Proceedings of the Second International Conference, pages 230-237, San
Mateo, California, April 22-25 1991. Morgan Kaufman.
-
[GM78] H. Gallaire and J. Minker, editors. Logic and Databases. Plenum Press, New York, April
1978.
-
[GPP86] M. Gelfond, H. Przymusinska, and T.C. Przymusinski. The extended closed world as-
sumption and its relation to parallel circumscription. Proc. Fifth ACM SIGACT-SIGMOD
Symposium on Principle of Database Systems, pages 133-139, 1986.
-
[GPP89] M. Gelfond, H. Przymusinska, and T.C. Przymusinski. On the relationship between cir-
cumscription and negation as failure. Artificial Intelligence., 38(1), 75-94, 1989.
-
[GS90] J. Grant and V.S. Subrahmanian. Reasoning in inconsistent knowledge bases. to appear
in IEEE Trans. Knowledge and Data Engineering.
-
[Gef89] H. Geffner. Default Reasoning: Causal and Conditional Theories. Ph.D thesis, Computer
Science Department, UCLA, 1989.
-
[Gel87] M. Gelfond. On stratified autoepistemic theories. In Proc. AAAI-87, pages 207-211, 1987.
-
[Gel92] M. Gelfond. Logic programming and reasoning with incomplete information. Technical
report, Dept of Computer Science, University of Texas at El Paso, 1992.
-
[Gin86] M. Ginsberg. Counterfactuals. Artificial Intelligence, 30:35-79, 1986.
-
[Gin87A] M. Ginsberg. Readings in Nonmonotonic Reasoning. Morgan Kaufmann, Los Altos, Cal-
ifornia, 1987.
-
[Gin89] M. Ginsberg. A circumscriptive theorem prover. Artificial Intelligence, 39:265-316, 1989.
-
[Gin91] M. Ginsberg. The MVL theorem proving system. SIGART Bulletin: Special Issue on
implemented knowledge representation and reasoning systems, 2(3):57-60, 1991.
-
[Gir92] F. Gire. Well founded semantics and stable semantics of semi-strict programs. In Interna-
tional Conference on Database Theory: Lecture Notes in Computer Science 646, Springer
Verlag, pages 261-275, 1992.
-
[Got91] G. Gottlob. Complexity results for nonmonotonic logics. Technical report, Institut fur
Informationssysteme, Technishe Universitat, Wien, 1991.
-
[Gro91] B. Grosof. Generalizing prioritization. In J. Allen, R. Fikes, and E. Sandewall, editors,
Principles of Knowledge Representation and Reasoning: Proceedings of the Second Inter-
national Conference, pages 289-300, San Mateo, California, April 22-25 1991. Morgan
Kaufman.
-
[HP87] L. Henschen and H. Park. Compiling the GCWA in Indefinite Deductive Databases. In
J. Minker, editor, Foundations of Deductive Databases and Logic Programming, pages
395-439. Morgan Kaufmann Pub., Washington, D.C., 1988.
-
[HT92] J. Horty and R. Thomason. Conditionals and artificial intelligence. Fundamenta Infor-
matica (forthcoming), 1993.
-
[HTT90] J. Horty, R. Thomason, and D. Touretzky. A skeptical theory of inheritance in nonmono-
tonic semantic networks. Artificial Intelligence, 42:311-348, 1990. abbreviated version
appears in Proceedings of AAAI-87, Morgan Kaufmann, 358-363.
-
[Hay73] P.J. Hayes. Computation and deduction. In Proceedings of the Second Symposium on Math-
ematical Foundations of Computer Science, pages 105-118. Czechoslovakia: Czechoslo-
vakian Academy of Sciences, 1973.
-
[Hew69] C.E. Hewitt. PLANNER: A language for proving theorems in robots. First International
Joint Conference on Artificial Intelligence, pages 295-301, 1969.
-
[IKH92] K. Inoue, M. Koshimura, and R. Hasegawa. Embedding negation as failure into a model
generation theorem prover. In International Conference on Automated Deduction (CADE-
11), pages 400-415, Saratoga Springs, NY, 1992.
-
[IOHN92] K. Inoue, Y. Ohta, R. Hasegawa and M. Nakashima. Bottom-Up abduction by model
generation. Technical Report TR-816, ICOT, Tokyo, October 1992.
-
[IOHN92] K. Inoue, Y. Ohta, R. Hasegawa, and M. Nakashima. Hypothetical reasoning systems on
the MGTP. Technical Report, ICOT, Tokyo (in Japanese), 1992.
-
[Imi87] T. Imielinski. Results on translating defaults to circumscription. Artificial Intelligence,
32:131-146, 1987.
-
[Ino90] K. Inoue. An abductive procedure for the CMS/ATMS. In Proc. European Conference on
Artificial Intelligence, ECAI 90 International Workshop on Truth Maintenance, Stockholm,
Springer Verlag Lecture Notes in Computer Science, 1990.
-
[Ino91a] K. Inoue. Hypothetical reasoning in logic programs. Technical Report ICOT 607, Tokyo,
1991.
-
[Ino91b] K. Inoue. Extended logic programs with default assumptions. In Proc. 8th International
Conference on Logic Programming, 490-504, Paris, 1991.
-
[Jer88] R.E. Jeroslow. Computation-Oriented Reductions of Predicate to Propositional Logic.
Decision Support Systems, 4, 183-187, 1988.
-
[KK89] M. Kifer and T. Krishnaprasad. An evidence based framework for a theory of inheri-
tance. In Proceedings of 11th Intl. Joint Conf. on Artificial Intelligence, pages 1093-1098,
Morgan-Kaufmann, 1989.
-
[KKT92] A.C. Kakas, R.A. Kowalski, and F. Toni. Abductive Logic Programming. Technical
Report, Dept. of Computing, Imperial College, London, Oct. 1992.
-
[KLM90] S. Kraus, D. Lehmann, and M. Magidor. Nonmonotonic reasoning, preferential models
and cumulative logics. Artificial Intelligence, 14(1):167-207, 1990.
-
[KM90] A.C. Kakas and P. Mancarella. Database updates through abduction. In Proc. 16th
International Conference on Very Large Databases, VLDB 90, Brisbane, Australia, 1990.
-
[KM91] A.C. Kakas and P. Mancarella. Stable theories for logic programs. In International Sym-
posium on Logic Programming, pages 85-100 1991.
-
[KPH91] S. Kraus, D. Perlis, and J. Horty. Reasoning about ignorance: A note on the bush-
gorbachev problem. Fundamenta Informaticae, 15:325-332, 1991.
-
[KS89] H.A. Kautz and B. Selman. Hard problems for simple default logics. In Proceedings of the
First International Conference on Principles of Knowledge Representation and Reasoning
(KR-89), pages 189-197, Toronto, Ontario, 1989.
-
[KS90] R. Kowalski and F. Sadri. Logic programs with exceptions. In Proc. 7th International
Conference on Logic Programming, Jerusalem, Israel, 598-613, 1990.
-
[Kon88] K. Konolige. On the relation between default and autoepistemic logic. Artificial Intelli-
gence, 35(3):343-382, July 1988.
-
[Kon90] K. Konolige Errata for: On the relation between default and autoepistemic logic. Artificial
Intelligence, 41:115, 1990.
-
[Kon91] K. Konolige. Quantification in autoepistemic logic. Fundamenta Informaticae, 15:275-300,
1991.
-
[Kri71] S. Kripke. Semantical considerations on modal logic. In L. Lindsay, editor, Reference and
Modality, pages 63-72, London, UK, 1971. Oxford University Press.
-
[Kun89] K. Kunen. Signed dependencies in logic programs. Journal of Logic Programming, 7,
231-245, 1989.
-
[LM92] D. Lehmann and M. Magidor. What does a conditional knowledge base entail? Artificial
Intelligence, 55(1), 1-60, May 1992.
-
[LMR92] J. Lobo, J. Minker, and A. Rajasekar. Foundations of Disjunctive Logic Programming.
MIT Press, 1992.
-
[LS89] F. Lin and Y. Shoham. Argument systems: A uniform basis for nonmonotonic reasoning.
In Proceedings of 1st Intl. Conference on Principles of Knowledge Representation and
Reasoning, pages 245-255, Stanford University, Stanford, CA, 1989.
-
[LS90] F. Lin and Y. Shoham. Epistemic semantics for fixed-points nonmonotonic logics. In
R. Parikh, editor, Theoretical Aspects of Reasoning and Knowledge: Proc. of the Third
Conf., pages 111-120, Stanford University, Stanford, CA, 1990.
-
[LS92] J. Lobo and V.S. Subrahmanian. Relating minimal models and pre-requisite-free normal
defaults. Information Processing Letters, 44:129-133, 1992.
-
[Lev84] H.J. Levesque. Foundations of a functional approach to knowledge representation. Artifi-
cial Intelligence, 23(2):155-212, 1984.
-
[Lev86] H.J. Levesque. Knowledge representation and reasoning. Annual Review of Computer
Science, 1:255-287, 1986.
-
[Lev90] H.J. Levesque. All I know: A study in Autoepistemic Logic. Artificial Intelligence 42,3/4,
(1990) pp. 263-309.
-
[Lew73] D. Lewis. Counterfactuals. Oxford University Press, 1973.
-
[Lif85] V. Lifschitz. Computing circumscription. In Proceedings of IJCAI-85, pages 121-127,
1985.
-
[Lif86] V. Lifschitz. Pointwise circumscription: a preliminary report. In Proc. Amer. Assoc. for
Art. Intell. National Conf., pages 406-410, Philadelphia, 1986.
-
[Lif89a] V. Lifschitz. Benchmark problems for formal nonmonotonic reasoning. In Nonmonotonic
Reasoning: 2nd Intl. Workshop, pages 202-217, 1989. (Lecture Notes in Artificial Intelli-
gence 346).
-
[Lif89b] V. Lifschitz. Between circumscription and autoepistemic logic. Research Report, Stanford
University, Stanford, CA (1989).
-
[Lif91] V. Lifschitz. Nonmonotonic databases and epistemic queries: Preliminary report. In Pro-
ceedings of 12th International Joint Conference on Artificial Intelligence, 381-386, Sydney,
Australia, 1991.
-
[Llo87] J.W. Lloyd. Foundations of Logic Programming, Springer-Verlag, Second Edition, 1987.
-
[Lob90] J. Lobo. On constructive negation for disjunctive logic programs. In Proc. North American
Conference on Logic Programming, 704-718, Austin, Texas, 1990.
-
[Luk90] W. Lukaszewicz Non-monotonic reasoning Ellis-Horwood, Chichester, West Sussex, Eng-
land, 1990.
-
[MD80] D. McDermott and J. Doyle. Non-monotonic logic I. Artificial Intelligence 25, pages
41-72, 1980.
-
[MD82] D. McDermott and J. Doyle. Non-monotonic logic II. Journal of the ACM, 29, pages
33-57, 1982.
-
[MH69] J. McCarthy and P.J. Hayes. Some philosophical problems from the standpoint of artificial
intelligence. In B. Meltzer and D. Michie, editors, Machine Intelligence 4, pages 463-502.
Edinburgh University Press, 1969.
-
[MLR91] J. Minker, J.Lobo, and A. Rajasekar. Circumscription and Disjunctive Logic Program-
ming. In Artificial Intelligence and Mathematical Theory of Computation, Papers in Honor
of John McCarthy, 281-305, Academic Press, 1991.
-
[MNR90] W. Marek, A. Nerode, and J. Remmel. A theory of non-monotonic rule systems, part i
(preliminary version). In Proc. 1990 Intl. Symp. on Logic in Computer Science, IEEE,
1990. Annals of Math. and AI. (to appear).
-
[MNR92] V. Marek, A. Nerode, and J.B. Remmel. The stable models of a predicate logic program. In
Proceedings of the Joint International Conference and Symposium on Logic Programming,
pages 446-460, 1992.
-
[MP85] J. Minker and D. Perlis. Computing protected circumscription. Journal of Logic Program-
ming, 2(4):235-249, December 1985.
-
[MR90] J. Minker and A. Rajasekar. A fixpoint semantics for disjunctive logic programs. Journal
of Logic Programming, 9(1):45-74, July 1990.
-
[MR93] J. Minker and C. Ruiz. On extended disjunctive logic programs. In Proceedings of the
Seventh International Symposium on Methodologies for Intelligent Systems, Norway, June
1993.
-
[MS91] W. Marek and V.S. Subrahmanian. The relationship between stable, supported, default
and auto-epistemic semantics for general logic programs. Theoretical Computer Science,
v.103(2), 365-386, Sept. 1992.
-
[MS92] W. Marek and V.S. Subrahmanian. The relationship between stable, supported, default
and autoepistemic semantics for general logic programs. Theoretical Computer Science,
103:365-386, 1992.
-
[MT89] W. Marek and M. Truszczy'nski. Relating autoepistemic and default logic. In Proceed-
ings of the First International Conference on Principles of Knowledge Representation and
Reasoning (KR-89), pages 276-288, Toronto, Ontario, 1989.
-
[MT91] V. Marek and M. Truszczynski. Autoepistemic logic. Journal of ACM, 38(3), 588-619,
July 1991.