Abstract
Logic programming has been deployed to support non-monotonic reasoning since the late ’80s. In this paper, we review semantics, formalisms and computational mechanisms for logic programming for non-monotonic reasoning. We also discuss some formalisms that have emerged from the cross fertilization between the two areas and some applications in as diverse areas as reasoning about dynamic domains, security, diagnosis and legal reasoning.
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References
Alberti, M., Chesani, F., Gavanelli, M., Lamma, E., Mello, P., Torroni, P.: Verifiable agent interaction in abductive logic programming: the SCIFF framework. ACM Transactions on Computational Logic (ToCL) 9(4) (2008)
Alferes, J.J., Dung, P.M., Pereira, L.M.: Scenario semantics of extended logic programs. In: LPNMR, pp. 334–348 (1993)
Antoniou, G., Baldoni, M., Bonatti, P.A., Nejdl, W., Olmedilla, D.: Rule-based policy specification. In: Secure Data Management in Decentralized Systems. Advances in Information Security, vol. 33, pp. 169–216. Springer, Heidelberg (2007)
Antoniou, G., Billington, D., Governatori, G., Maher, M.J.: Embedding defeasible logic into logic programming. TPLP 6(6), 703–735 (2006)
Baier, J.A., McIlraith, S.A.: On planning with programs that sense. In: KR, pp. 492–502 (2006)
Baldoni, M., Baroglio, C., Mascardi, V., Omicini, A., Torroni, P.: Agents, Multi-Agent Systems and Declarative Programming: What, When, Where, Why, Who, How? In: Dovier, A., Pontelli, E. (eds.) 25 Years of Logic Programming in Italy, ch. 10. LNCS, vol. 6125, pp. 204–230. Springer, Heidelberg (2010)
Baldoni, M., Martelli, A., Patti, V., Giordano, L.: Programming rational agents in a modal action logic. Ann. Math. Artif. Intell. 41(2-4), 207–257 (2004)
Bandara, A.K., Kakas, A.C., Lupu, E.C., Russo, A.: Using argumentation logic for firewall policy specification and analysis. In: State, R., van der Meer, S., O’Sullivan, D., Pfeifer, T. (eds.) DSOM 2006. LNCS, vol. 4269, pp. 185–196. Springer, Heidelberg (2006)
Baral, C., Gelfond, M.: Logic programming and knowledge representation. Journal of Logic Programming 19, 73–148 (1994)
Baral, C., Gelfond, M.: Reasoning agents in dynamic domains, pp. 257–279 (2000)
Baral, C., Gelfond, M., Provetti, A.: Representing actions: Laws, observations and hypotheses. J. Log. Program. 31(1-3), 201–243 (1997)
Baral, C., McIlraith, S., Son, T.: Formulating diagnostic problem solving using an action language with narratives and sensing. In: Proceedings of the Seventh International Conference on Principles of Knowledge Representation and Reasoning (KR 2000), Breckenridge, Colorado, USA, April 12-15, pp. 311–322 (2000)
Belleghem, K.V., Denecker, M., Schreye, D.D.: On the relation between situation calculus and event calculus. J. Log. Program. 31(1-3), 3–37 (1997)
Bonatti, P., Calimeri, F., Leone, N., Ricca, F.: Answer Set Programming. In: Dovier, A., Pontelli, E. (eds.) 25 Years of Logic Programming in Italy, ch. 8. LNCS, vol. 6125, pp. 159–182. Springer, Heidelberg (2010)
Bonatti, P.A.: Autoepistemic logic programming. J. Autom. Reasoning 13(1), 35–67 (1994)
Bonatti, P.A.: Reasoning with infinite stable models. Artif. Intell. 156(1), 75–111 (2004)
Bonatti, P.A., Duma, C., Fuchs, N., Nejdl, W., Olmedilla, D., Peer, J., Shahmehri, N.: Semantic web policies – A discussion of requirements and research issues. In: Sure, Y., Domingue, J. (eds.) ESWC 2006. LNCS, vol. 4011, pp. 712–724. Springer, Heidelberg (2006)
Bondarenko, A., Dung, P.M., Kowalski, R.A., Toni, F.: An abstract, argumentation-theoretic approach to default reasoning. Artificial Intelligence 93(1-2), 63–101 (1997)
Bondarenko, A., Toni, F., Kowalski, R.: An assumption-based framework for non-monotonic reasoning. In: Nerode, A., Pereira, L. (eds.) Proc. 2nd International Workshop on Logic Programming and Non-monotonic Reasoning, pp. 171–189. MIT Press, Cambridge (1993)
Buccafurri, F., Leone, N., Rullo, P.: Stable models and their computation for logic programming with inheritance and true negation. J. Log. Program. 27(1), 5–43 (1996)
Cervesato, I., Franceschet, M., Montanari, A.: A guided tour through some extensions of the Event Calculus. Computational Intelligence 16(2), 307–347 (2000)
Cervesato, I., Montanari, A.: A general modal framework for the Event Calculus and its skeptical and creduluos variants. J. Log. Program. 38(2), 111–164 (1999)
Chandra, A., Harel, D.: Horn clause queries and generalizations. Journal of Logic Programming 2(1), 1–5 (1985)
Chen, W., Warren, D.S.: Computation of stable models and its integration with logical query processing. IEEE Transactions on Knowledge and Data Engineering 8, 8–5 (1994)
Chittaro, L., Montanari, A., Provetti, A.: Skeptical and credoluos event calculi for supporting modal queries. In: ECAI 1994, pp. 361–365 (1994)
Christiansen, H., Dahl, V.: HYPROLOG: A new logic programming language with assumptions and abduction. In: Gabbrielli, M., Gupta, G. (eds.) ICLP 2005. LNCS, vol. 3668, pp. 159–173. Springer, Heidelberg (2005)
Clark, K.L.: Negation as failure. In: Logic and Data Bases. Plenum Press (1978)
Console, L., Dupré, D.T., Torasso, P.: A theory of diagnosis for incomplete causal models. In: IJCAI, pp. 1311–1317 (1989)
Console, L., Dupre, D.T., Torasso, P.: On the relationship between abduction and deduction. Journal of Logic and Computation 1(5), 661–690 (1991)
Console, L., Torasso, P.: A spectrum of logical definitions of model-based diagnosis. Computational Intelligence 7, 133–141 (1991)
Costantini, S.: Contributions to the stable model semantics of logic programs with negation. Theor. Comput. Sci. 149(2), 231–255 (1995)
Costantini, S.: On the existence of stable models of non-stratified logic programs. TPLP 6(1-2), 169–212 (2006)
Dantsin, E., Eiter, T., Gottlob, G., Voronkov, A.: Complexity and expressive power of logic programming. ACM Comput. Surv. 33(3), 374–425 (2001)
De Giacomo, G., Lesperance, Y., Levesque, H.J.: Reasoning about concurrent execution, prioritized interrupts, and exogenous actions in the situation calculus. In: IJCAI 1997: Proceedings of the Fifteenth international joint conference on Artifical intelligence, pp. 1221–1226. Morgan Kaufmann Publishers Inc., San Francisco (1997)
De Giacomo, G., Levesque, H.J.: An incremental interpreter for high-level programs with sensing. In: Logical Foundations for Cognitive Agents, pp. 86–102. Springer, Heidelberg (1998)
de Kleer, J.: An assumption-based tms. Artif. Intell. 28(2), 127–162 (1986)
Denecker, M., Bruynooghe, M., Marek, V.W.: Minimal belief and negation as failure. ACM Trans. Comput. Log. 2(4), 623–654 (2001)
Denecker, M., Dupré, D.T., Belleghem, K.V.: An inductive definition approach to ramifications. Electron. Trans. Artif. Intell. 2, 25–67 (1998)
Denecker, M., Kakas, A.C.: Abduction in Logic Programming. In: Kakas, A.C., Sadri, F. (eds.) Computational Logic: Logic Programming and Beyond, Part I. LNCS (LNAI), vol. 2407, pp. 402–436. Springer, Heidelberg (2002)
Denecker, M., Schreye, D.D.: Representing incomplete knowledge in abductive logic programming. In: Proc. of the International Symposium on Logic Programming, pp. 147–163. MIT Press, Cambridge (1993)
Denecker, M., Schreye, D.D.: SLDNFA: an abductive procedure for abductive logic programs. Journal of Logic Programming 34(2), 111–167 (1998)
Dovier, A., Pontelli, E. (eds.): 25 Years of Logic Programming in Italy. LNCS, vol. 6125. Springer, Heidelberg (2010)
Doyle, J.: A truth maintenance system. Artif. Intell. 12(3), 231–272 (1979)
Dung, P.: On the acceptability of arguments and its fundamental role in nonmonotonic reasoning, logic programming, and n-person games. Artificial Intelligence 77(2), 321–357 (1995)
Dung, P., Kowalski, R., Toni, F.: Assumption-based argumentation. In: Rahwan, I., Simari, G. (eds.) Argumentation in AI: The Book. Springer, Heidelberg (2009) (to appear)
Dung, P.M.: Negations as hypotheses: An abductive foundation for logic programming. In: ICLP, pp. 3–17 (1991)
Dung, P.M.: Representing actions in logic programming and its applications in database updates. In: ICLP, pp. 222–238 (1993)
Dung, P.M., Mancarella, P., Toni, F.: Computing ideal sceptical argumentation. Artificial Intelligence 171(10-15), 642–674 (2007)
Eshghi, K., Kowalski, R.A.: Abduction compared with negation by failure. In: ICLP, pp. 234–254 (1989)
Fitting, M.: A Kripke/Kleene semantics for logic programs. Journal of Logic Programming 2, 295–312 (1985)
Fung, T.H., Kowalski, R.A.: The IFF proof procedure for abductive logic programming. Journal of Logic Programming 33(2), 151–165 (1998)
Gabbay, D.M., Giordano, L., Martelli, A., Olivetti, N., Sapino, M.L.: Conditional reasoning in logic programming. J. Log. Program. 44(1-3), 37–74 (2000)
Gaertner, D., Toni, F.: Hybrid argumentation and its properties. In: Hunter, A. (ed.) Proceedings of the Second International Conference on Computational Models of Argument (COMMA 2008), pp. 183–195. IOS Press, Amsterdam (2008)
García, A.J., Dix, J., Simari, G.R.: Argument-based logic programming. In: Rahwan, I., Simari, G. (eds.) Argumentation in AI: The Book. Springer, Heidelberg (2009) (to appear)
Gavanelli, M., Rossi, F.: Constraint Logic Programming. In: Dovier, A., Pontelli, E. (eds.) 25 Years of Logic Programming in Italy, ch. 4. LNCS, vol. 6125, pp. 64–86. Springer, Heidelberg (2010)
Gelder, A.V., Ross, K.A., Schlipf, J.S.: Unfounded sets and well-founded semantics for general logic programs. In: PODS, pp. 221–230 (1988)
Gelfond, M., Lifschitz, V.: The stable model semantics for logic programming. In: Kowalski, R., Bowen, K. (eds.) Proceedings of the Fifth International Conference and Symposium on Logic Programming, pp. 1070–1080. MIT Press, Cambridge (1988)
Gelfond, M., Lifschitz, V.: Representing action and change by logic programs. Journal of logic Programming 17, 301–322 (1993)
Gelfond, M., Lifschitz, V.: Action languages. Electronic Transactions on AI 3(16), 193–210 (1998)
Giacomo, G.D., Lenzerini, M.: PDL-based framework for reasoning about actions. In: AI*IA, pp. 103–114 (1995)
Giordano, L., Martelli, A.: Generalized stable models, truth maintenance and conflict resolution. In: ICLP, pp. 427–441 (1990)
Giordano, L., Martelli, A., Schwind, C.: Ramification and causality in a modal action logic. J. Log. Comput. 10(5), 625–662 (2000)
Giordano, L., Martelli, A., Schwind, C.: Specifying and verifying interaction protocols in a temporal action logic. J. Applied Logic 5(2), 214–234 (2007)
Giordano, L., Olivetti, N.: Combining negation as failure and embedded implications in logic programs. J. Log. Program. 36(2), 91–147 (1998)
Giunchiglia, E., Lee, J., Lifschitz, V., McCain, N., Turner, H.: Nonmonotonic causal theories. Artif. Intell. 153(1-2), 49–104 (2004)
Giunchiglia, E., Lifschitz, V.: An action language based on causal explanation: Preliminary report. In: AAAI/IAAI, pp. 623–630 (1998)
Governatori, G.: Representing business contracts in ruleml. Int. J. Cooperative Information Systems 14(2-3), 180–216 (2005)
Governatori, G., Rotolo, A.: Defeasible logic: Agency, intention and obligation. In: Lomuscio, A., Nute, D. (eds.) DEON 2004. LNCS (LNAI), vol. 3065, pp. 114–128. Springer, Heidelberg (2004)
Greco, S., Lisi, F.: Logic Programming Languages for Databases and the Web. In: Dovier, A., Pontelli, E. (eds.) 25 Years of Logic Programming in Italy, ch. 9. LNCS, vol. 6125, pp. 183–203. Springer, Heidelberg (2010)
Hanks, S., McDermott, D.V.: Nonmonotonic logic and temporal projection. Artif. Intell. 33(3), 379–412 (1987)
Kakas, A., Mancarella, P.: Generalized stable models: A semantics for abduction. In: ECAI, pp. 385–391 (1990)
Kakas, A.C., Kowalski, R.A., Toni, F.: Abductive logic programming. Journal of Logic and Computation 2(6), 719–770 (1993)
Kakas, A.C., Kowalski, R.A., Toni, F.: The role of abduction in logic programming. In: Handbook of Logic in Artificial Intelligence and Logic Programming, vol. 5, pp. 235–324. OUP (1998)
Kakas, A.C., Mancarella, P.: Generalized stable models: a semantics for abduction. In: Proceedings of the 9th European Conference on Artificial Intelligence, pp. 385–391 (1990)
Kakas, A.C., Mancarella, P.: Short note: Preferred extensions are partial stable models. J. Log. Program. 14(3&4), 341–348 (1992)
Kakas, A.C., Van Nuffelen, B., Denecker, M.: A-system: Problem solving through abduction. In: Proceedings of the 17th International Joint Conference on Artificial Intelligence, pp. 591–596 (2001)
Kifer, M.: Nonmonotonic Reasoning in FLORA-2. In: Baral, C., Greco, G., Leone, N., Terracina, G. (eds.) LPNMR 2005. LNCS (LNAI), vol. 3662, pp. 1–12. Springer, Heidelberg (2005)
Kowalski, R., Sergot, M.: A logic-based calculus of events. New Generation Computing 4(1), 67–95 (1986)
Kowalski, R.A.: Predicate logic as programming language. In: IFIP Congress, pp. 569–574 (1974)
Kowalski, R.A., Kuehner, D.: Linear resolution with selection function. Artif. Intell. 2(3/4), 227–260 (1971)
Kowalski, R.A., Toni, F.: Abstract argumentation. Artif. Intell. Law 4(3-4), 275–296 (1996)
Kunen, K.: Negation in logic programming. Journal of Logic Programming 4(4), 289–308 (1987)
Kunen, K.: Signed data dependencies in logic programs. J. Log. Program. 7(3), 231–245 (1989)
Leone, N., Rullo, P.: Ordered logic programming with sets. J. Log. Comput. 3(6), 621–642 (1993)
Levesque, H., Reiter, R., Lespérance, Y., Lin, F., Scherl, R.: Golog: A logic programming language for dynamic domains. Journal of Logic Programming 31, 59–83 (1997)
Li, R., Pereira, L.M.: Representing and reasoning about concurrent actions with abductive logic programs. Ann. Math. Artif. Intell. 21(2-4), 245–303 (1997)
Lifschitz, V.: Minimal belief and negation as failure. Artificial Intelligence 70(1-2), 53–72 (1994)
Lin, F.: Embracing causality in specifying the indirect effects of actions. In: IJCAI, pp. 1985–1993 (1995)
Lloyd, J.W.: Foundations of Logic Programming, 1st edn. Springer, Heidelberg (1984)
Mancarella, P., Terreni, G., Sadri, F., Toni, F., Endriss, U.: The CIFF proof procedure for abductive logic programming with constraints: Theory, implementation and experiments. Theory and Practice of Logic Programming 9(6), 691–750 (2009)
McCain, N., Turner, H.: A causal theory of ramifications and qualifications. In: IJCAI, pp. 1978–1984 (1995)
McCarthy, J.: Situations actions and causal laws. Technical Report. Stanford (1963); Reprinted in Semantic Information Processing (Minsky, M. (ed.)), pp. 410-417. MIT Press, Cambridge (1968)
McCarthy, J.: Circumscription—a form of non-monotonic reasoning. Artificial Intelligence 13, 27–39 (1980)
McDermott, D.V.: Nonmonotonic logic ii: Nonmonotonic modal theories. J. ACM 29(1), 33–57 (1982)
Minker, J.: An overview of nonmonotonic reasoning and logic programming. Journal of Logic Programming, Special Issue 17, 95–126 (1993)
Moore, R.C.: Semantical considerations on nonmonotonic logic. Artif. Intell. 25(1), 75–94 (1985)
Nebel, B.: Belief revision and default reasoning: Syntax-based approaches. In: KR, pp. 417–428 (1991)
Niemel, I., Simons, P.: Efficient implementation of the well-founded and stable model semantics. In: Proceedings of the Joint International Conference and Symposium on Logic Programming, pp. 289–303. MIT Press, Cambridge (1996)
Nitta, K., Shibasaki, M.: Defeasible reasoning in japanese criminal jurisprudence. Artif. Intell. Law 5(1-2), 139–159 (1997)
Noël, V., Kakas, A.C.: Gorgias-c: Extending argumentation with constraint solving. In: Erdem, E., Lin, F., Schaub, T. (eds.) LPNMR 2009. LNCS, vol. 5753, pp. 535–541. Springer, Heidelberg (2009)
Nute, D.: Defeasible logic. In: Bartenstein, O., Geske, U., Hannebauer, M., Yoshie, O. (eds.) INAP 2001. LNCS (LNAI), vol. 2543, pp. 87–114. Springer, Heidelberg (2003)
Pednault, E.P.D.: Adl: Exploring the middle ground between strips and the situation calculus. In: KR, pp. 324–332 (1989)
Pereira, L.M., Alferes, J.J., Aparício, J.N.: Contradiction removal semantics with explicit negation. In: Masuch, M., Polos, L. (eds.) Logic at Work 1992. LNCS, vol. 808. Springer, Heidelberg (1994)
Poole, D.: A logical framework for default reasoning. Artif. Intell. 36(1), 27–47 (1988)
Prakken, H., Sartor, G.: A dialectical model of assessing conflicting arguments in legal reasoning. Artif. Intell. Law 4(3-4), 331–368 (1996)
Prakken, H., Sartor, G.: Argument-based extended logic programming with defeasible priorities. Journal of Applied Non-classical Logics 7, 25–75 (1997)
Prakken, H., Sartor, G.: The Role of Logic in Computational Models of Legal Argument: A Critical Survey. In: Kakas, A.C., Sadri, F. (eds.) Computational Logic: Logic Programming and Beyond, Part II. LNCS (LNAI), vol. 2408, pp. 342–381. Springer, Heidelberg (2002)
Prakken, H., Sartor, G.: Formalising arguments about the burden of persuasion. In: ICAIL-The Eleventh International Conference on Artificial Intelligence and Law, Proceedings of the Conference, Stanford Law School, Stanford, California, USA, June 4-8, pp. 97–106. ACM, New York (2007)
Preist, C., Eshghi, K.: Consistency-based and abductive diagnoses as generalised stable models. In: FGCS, pp. 514–521 (1992)
Prendinger, H., Schurz, G.: Reasoning about action and change. A dynamic logic approach. Journal of Logic, Language and Information 5(2), 209–245 (1996)
Przymusinski, T.C.: Perfect model semantics. In: ICLP/SLP, pp. 1081–1096 (1988)
Przymusinski, T.C.: Extended stable semantics for normal and disjunctive programs. In: ICLP, pp. 459–477 (1990)
Reiter, R.: On closed world data bases. In: Logic and Data Bases, pp. 55–76 (1977)
Reiter, R.: A logic for default reasoning. Artificial Intelligence 13(1-2), 81–132 (1980)
Reiter, R.: Circumscription implies predicate completion (sometimes). In: AAAI, pp. 418–420 (1982)
Reiter, R.: A theory of diagnosis from first principles. Artif. Intell. 32(1), 57–95 (1987)
Reiter, R.: Knowledge in action. MIT Press, Cambridge (2001)
Saccà, D., Zaniolo, C.: Stable models and non-determinism in logic programs with negation. In: Proceedings of the Ninth ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems, Nashville, Tennessee, April 2-4, pp. 205–217. ACM Press, New York (1990)
Sadri, F., Kowalski, R.A.: Variants of the event calculus. In: ICLP, pp. 67–81 (1995)
Sadri, F., Toni, F.: Interleaving belief updating and reasoning in abductive logic programming. In: Brewka, G., Coradeschi, S., Perini, A., Traverso, P. (eds.) Proceedings of the 17th European Conference on Artificial Intelligence (ECAI 2006), Riva del Garda, Italy, 28 August–1 September 2006. IOS Press, Amsterdam (2006)
Sergot, M.J., Sadri, F., Kowalski, R.A., Kriwaczek, F., Hammond, P., Cory, H.T.: The british nationality act as a logic program. Commun. ACM 29(5), 370–386 (1986)
Shanahan, M.: Solving the frame problem: A mathematical investigation of the common sense law of inertia. MIT Press, Cambridge (1997)
Shanahan, M.: An abductive event calculus planner. J. Log. Program. 44(1-3), 207–240 (2000)
Shepherdson, J.C.: Negation as failure: A comparison of clark’s completed data base and reiter’s closed world assumption. J. Log. Program. 1(1), 51–79 (1984)
Shepherdson, J.C.: Negation as failure ii. J. Log. Program. 2(3), 185–202 (1985)
Thielscher, M.: Ramification and causality. Artif. Intell. 89(1-2), 317–364 (1997)
Thielscher, M.: From situation calculus to fluent calculus: State update axioms as a solution to the inferential frame problem. Artif. Intell. 111(1-2), 277–299 (1999)
Toni, F.: A semantics for the Kakas-Mancarella procedure for abductive logic programming. In: Alpuente, M., Sessa, M.I. (eds.) 995 Joint Conference on Declarative Programming, GULP-PRODE 1995, Marina di Vietri, Italy, September 11-14, pp. 231–244 (1995)
Van Gelder, A., Ross, K., Schlifp, J.: The well-founded semantics for general logic programs. Journal of ACM 38(3), 620–650 (1991)
Witteveen, C., Brewka, G.: Skeptical reason maintenance and belief revision. Artif. Intell. 61(1), 1–36 (1993)
You, J.-H., Cartwright, R., Li, M.: Iterative belief revision in extended logic programming. Theoretical Computer Science, 170–171 (1996)
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Giordano, L., Toni, F. (2010). Knowledge Representation and Non-monotonic Reasoning . In: Dovier, A., Pontelli, E. (eds) A 25-Year Perspective on Logic Programming. Lecture Notes in Computer Science, vol 6125. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14309-0_5
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