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Epistemic Logic for Rule-Based Agents

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Abstract

The logical omniscience problem, whereby standard models of epistemic logic treat an agent as believing all consequences of its beliefs and knowing whatever follows from what else it knows, has received plenty of attention in the literature. But many attempted solutions focus on a fairly narrow specification of the problem: avoiding the closure of belief or knowledge, rather than showing how the proposed logic is of philosophical interest or of use in computer science or artificial intelligence. Sentential epistemic logics, as opposed to traditional possible worlds approaches, do not suffer from the problems of logical omniscience but are often thought to lack interesting epistemic properties. In this paper, I focus on the case of rule-based agents, which play a key role in contemporary AI research but have been neglected in the logical literature. I develop a framework for modelling monotonic, nonmonotonic and introspective rule-based reasoners which have limited cognitive resources and prove that the resulting models have a number of interesting properties. An axiomatization of the resulting logic is given, together with completeness, decidability and complexity results.

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References

  • Ågotnes, T. (2004). A logic of finite syntactic epistemic states. Ph.D. thesis, Department of Informatics, University of Bergen, Norway.

  • Ågotnes, T., & Alechina, N. (2005). The dynamics of syntactic knowledge. Technical Report 304, Department of Informatics, University of Bergen, Norway.

  • Ågotnes, T., & Walicki, M. (2004). Syntactic knowledge: A logic of reasoning, communication and cooperation. In Proceedings of the Second European Workshop on Multi-Agent Systems (EUMAS 2004).

  • Aiken A., Widom J., Hellerstein J. (1992) Behavior of database production rules: termination, confluence, and observable determinism. ACM SIGMOD Record 21(2): 59–68

    Article  Google Scholar 

  • Alechina, N., Bordini, R., Hubner, J., Jago, M., & Logan, B. (2006a). Automating belief revision for agentspeak. In M. Baldoni & U. Endriss (Eds.), Declarative agent languages and technologies IV, DALT 2006, selected, revised and invited papers (Vol. LNAI 4327, pp. 61–77). Springer.

  • Alechina, N., Jago, M., & Logan, B. (2006b). Modal logics for communicating rule-based agents. In G. Brewka, S. Coradeschi, A. Perini, & P. Traverso (Eds.), Proceedings of the 17th European Conference on Artificial Intelligence (ECAI 2006) (pp. 322–326). IOS Press.

  • Alechina, N., Logan, B., & Whitsey, M. (2004a). A complete and decidable logic for resource-bounded agents. In Proceedings of the Third International Joint Conference on Autonomous Agents and Multi-Agent Systems (AAMAS 2004) (pp. 606–613). ACM Press.

  • Alechina, N., Logan, B., & Whitsey, M. (2004b). Modelling communicating agents in timed reasoning logics. In Proceedings of JELIA 04 (pp. 95–107).

  • Alur R., Henzinger T., Kupferman O. (2002) Alternating-time temporal logic. Journal of the ACM 49: 672–713

    Article  Google Scholar 

  • Bellifemine F., Poggi A., Rimassa G. (2001) Developing multi-agent systems with a FIPA-compliant agent framework. Software Practice and Experience 21(2): 103–128

    Article  Google Scholar 

  • Blackburn P., de Rijke M., Venema Y. (2002) Modal logic. Cambridge University Press, New York

    Google Scholar 

  • Brcommunity.com (2006). Business rules community website, http://www.brcommunity.com/. Accessed 13th March.

  • CLIPS. (2003). CLIPS reference manual: Version 6.21. Software Technology Branch, Lyndon B. Johnson Space Center, Houston.

  • Corazza, E. (2004). Reflecting the mind: Indexicality and quasi-indexicality. Oxford University Press.

  • Davidson, D. (1968). On saying that. In Truth and interpretation (pp. 93–108). Oxford: Basil Blackwell.

  • Duc, H. N. (1995). Logical omniscience vs. logical ignorance. In: C. Pereira & N. Mamede (Eds.), Proceedings of EPIA’95 (Vol. 990 of LNAI. pp. 237–248). Springer.

  • Duc H.N. (1997) Reasoning about rational, but not logically omniscient, agents. Journal of Logic and Computation 5: 633–648

    Article  Google Scholar 

  • Elgot-Drapkin, J., Kraus, S., Miller, M., Nirkhe, M., & Perlis, D. (1999). Active logics: A unified formal approach to episodic reasoning. Technical Report CS-TR-4072, University of Maryland, Department of Computer Science.

  • Elgot-Drapkin J., Miller M., Perlis D. (1991) Memory, reason and time: the Step-Logic approach. In: Cummins R., Pollock J.(eds) Philosophy and AI: Essays at the interface. MIT Press, Cambridge, Mass, pp 79–103

    Google Scholar 

  • Emerson E., Halpern J. (1982) Decision procedures and expressiveness in the temporal logic of branching time. Journal of computer and system sciences 30(1): 1–24

    Article  Google Scholar 

  • Fagin R., Halpern J. (1988) Belief, awareness and limited reasoning. Artificial Intelligence 34: 39–76

    Article  Google Scholar 

  • Fagin, R., Halpern, J., Moses, Y., & Vardi, M. (1995). Reasoning about knowledge. MIT press.

  • Fagin, R., Halpern, J., & Vardi, M. (1990). A nonstandard approach to the logical omniscience problem. In: R. Parikh (Ed.), Proceedings of the Third Conference on Theoretical Aspects of Reasoning about Knowledge (pp. 41–55). Morgan Kaufmann.

  • Fodor J. (1990) A theory of content and other essays. MIT Press, Cambridge, Mass

    Google Scholar 

  • Ginsberg, M. (1994). AI and nonmonotonic reasoning. In D. G. et al. (Eds.), Handbook of logic in artificial intelligence and logic programming. Volume 3: Nonmonotonic reasoning and uncertain reasoning (pp. 1–33). Oxford: Clarendon Press.

  • Grant, J., Kraus, S., & Perlis, D. (2000). A logic for characterizing multiple bounded agents. In Autonomous agents and multi-agent systems (pp. 351–387).

  • Hintikka J. (1962) Knowledge and belief: an introduction to the logic of the two notions. Cornell University Press, Ithaca, N.Y

    Google Scholar 

  • Jago, M. (2006). Logics for resource-bounded agents. Ph.D. thesis, University of Nottingham.

  • Kaplan D., Montague R. (1960) A paradox regained. Notre Dame Journal of Symbolic Logic 1: 79–90

    Article  Google Scholar 

  • Konolige, K. (1986). A deduction model of belief. Morgan Kaufman.

  • Laird J.E., Newell A., Rosenbloom P.S. (1987) SOAR: An architecture for general intelligence. Artificial Intelligence 33: 1–64

    Article  Google Scholar 

  • Levesque, H. J. (1984). A logic of implicit and explicit belief. In National Conference on Artificial Intelligence (pp. 1998–202).

  • Loewer B., Lepore E. (1989) You can say that again. Midwest Studies in Philosophy 14: 338–356

    Article  Google Scholar 

  • Makinson, D. (2005). Bridges from classical to nonmonotonic logic, Vol. 5 of texts in computing. King’s College Publications.

  • McCarthy, J. (1979). First order theories of individual concepts and propositions. In D. M. J. E. Hayes & L. Mikulick, (Eds.), Machine Intelligence (Vol. 9, pp. 129–147). New York: Halstead Press.

  • Nirkhe, M., Kraus, S., & Perlis, D. (1994). Thinking takes time: A modal active-logic for reasoning in time. Technical Report CS-TR-3249, University of Maryland, Department of Computer Science.

  • Perry J. (1980) Belief and acceptance. Midwest Studies in Philosophy 5: 553–554

    Article  Google Scholar 

  • Poslad, S., Buckle, P., & Hadingham, R. G. (2000). The FIPA-OS agent platform: Open source for open standards. In Proceedings of the Fifth International Conference and Exhibition on the Practical Application of Intelligent Agents and Multi-Agents (PAAM2000) (pp. 355–368). Manchester.

  • Priest G. (2005) Towards non-being. Clarendon Press, Oxford

    Google Scholar 

  • Quine W. (1960) Word and object. MIT Press, Cambridge, Mass

    Google Scholar 

  • Sloman A., Logan B. (1999) Building cognitively rich agents using the SIM AGENT toolkit. Communications of the ACM 42(3): 71–77

    Article  Google Scholar 

  • Stalnaker R. (1991) The problem of logical omniscience I. Synthese 89: 425–440

    Article  Google Scholar 

  • Stich S. (1983) From folk psychology to cognitive science. MIT press, Cambridge, Mass

    Google Scholar 

  • Thomason R. (1980) A note on syntactical treatments of modality. Synthese 44: 391–395

    Article  Google Scholar 

  • van Benthem, J. (2008). Tell it like it is: information flow in logic. ILLC prepublication series, pp-2008-08, http://www.illc.uva.nl/Publications/ResearchReports/PP-2008-08.text.pdf.

  • van Ditmarsch, H., van der Hoek, W., & Kooi, B. (2007). Dynamic epistemic logic, Vol. 337 of Synthese Library. Springer.

  • Vianu V. (1997) Rule-based languages. Annals of Mathematics and Artificial Intelligence 19: 215–259

    Article  Google Scholar 

  • Whitsey, M. (2004). Modelling resource bounded reasoners: An example. In Proceedings of the Logic and Communication in Multi-Agent Systems workshop (LCMAS 04) (pp. 118–137). Loria.

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  1. Department of Philosophy, Macquarie University, Sydney, NSW, 2109, Australia

    Mark Jago

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Jago, M. Epistemic Logic for Rule-Based Agents. J of Log Lang and Inf 18, 131–158 (2009). https://doi.org/10.1007/s10849-008-9071-8

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