Journal of Logic, Language and Information

, Volume 18, Issue 1, pp 131–158 | Cite as

Epistemic Logic for Rule-Based Agents

Article

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.

Keywords

Epistemic logic Doxastic logic Rule-based agents Resource bounds Artificial intelligence Logical omniscience 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Ågotnes, T. (2004). A logic of finite syntactic epistemic states. Ph.D. thesis, Department of Informatics, University of Bergen, Norway.Google Scholar
  2. Ågotnes, T., & Alechina, N. (2005). The dynamics of syntactic knowledge. Technical Report 304, Department of Informatics, University of Bergen, Norway.Google Scholar
  3. 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).Google Scholar
  4. Aiken A., Widom J., Hellerstein J. (1992) Behavior of database production rules: termination, confluence, and observable determinism. ACM SIGMOD Record 21(2): 59–68CrossRefGoogle Scholar
  5. 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.Google Scholar
  6. 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.Google Scholar
  7. 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.Google Scholar
  8. Alechina, N., Logan, B., & Whitsey, M. (2004b). Modelling communicating agents in timed reasoning logics. In Proceedings of JELIA 04 (pp. 95–107).Google Scholar
  9. Alur R., Henzinger T., Kupferman O. (2002) Alternating-time temporal logic. Journal of the ACM 49: 672–713CrossRefGoogle Scholar
  10. Bellifemine F., Poggi A., Rimassa G. (2001) Developing multi-agent systems with a FIPA-compliant agent framework. Software Practice and Experience 21(2): 103–128CrossRefGoogle Scholar
  11. Blackburn P., de Rijke M., Venema Y. (2002) Modal logic. Cambridge University Press, New YorkGoogle Scholar
  12. Brcommunity.com (2006). Business rules community website, http://www.brcommunity.com/. Accessed 13th March.
  13. CLIPS. (2003). CLIPS reference manual: Version 6.21. Software Technology Branch, Lyndon B. Johnson Space Center, Houston.Google Scholar
  14. Corazza, E. (2004). Reflecting the mind: Indexicality and quasi-indexicality. Oxford University Press.Google Scholar
  15. Davidson, D. (1968). On saying that. In Truth and interpretation (pp. 93–108). Oxford: Basil Blackwell.Google Scholar
  16. 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.Google Scholar
  17. Duc H.N. (1997) Reasoning about rational, but not logically omniscient, agents. Journal of Logic and Computation 5: 633–648CrossRefGoogle Scholar
  18. 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.Google Scholar
  19. 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 79–103Google Scholar
  20. Emerson E., Halpern J. (1982) Decision procedures and expressiveness in the temporal logic of branching time. Journal of computer and system sciences 30(1): 1–24CrossRefGoogle Scholar
  21. Fagin R., Halpern J. (1988) Belief, awareness and limited reasoning. Artificial Intelligence 34: 39–76CrossRefGoogle Scholar
  22. Fagin, R., Halpern, J., Moses, Y., & Vardi, M. (1995). Reasoning about knowledge. MIT press.Google Scholar
  23. 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.Google Scholar
  24. Fodor J. (1990) A theory of content and other essays. MIT Press, Cambridge, MassGoogle Scholar
  25. 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.Google Scholar
  26. Grant, J., Kraus, S., & Perlis, D. (2000). A logic for characterizing multiple bounded agents. In Autonomous agents and multi-agent systems (pp. 351–387).Google Scholar
  27. Hintikka J. (1962) Knowledge and belief: an introduction to the logic of the two notions. Cornell University Press, Ithaca, N.YGoogle Scholar
  28. Jago, M. (2006). Logics for resource-bounded agents. Ph.D. thesis, University of Nottingham.Google Scholar
  29. Kaplan D., Montague R. (1960) A paradox regained. Notre Dame Journal of Symbolic Logic 1: 79–90CrossRefGoogle Scholar
  30. Konolige, K. (1986). A deduction model of belief. Morgan Kaufman.Google Scholar
  31. Laird J.E., Newell A., Rosenbloom P.S. (1987) SOAR: An architecture for general intelligence. Artificial Intelligence 33: 1–64CrossRefGoogle Scholar
  32. Levesque, H. J. (1984). A logic of implicit and explicit belief. In National Conference on Artificial Intelligence (pp. 1998–202).Google Scholar
  33. Loewer B., Lepore E. (1989) You can say that again. Midwest Studies in Philosophy 14: 338–356CrossRefGoogle Scholar
  34. Makinson, D. (2005). Bridges from classical to nonmonotonic logic, Vol. 5 of texts in computing. King’s College Publications.Google Scholar
  35. 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.Google Scholar
  36. 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.Google Scholar
  37. Perry J. (1980) Belief and acceptance. Midwest Studies in Philosophy 5: 553–554CrossRefGoogle Scholar
  38. 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.Google Scholar
  39. Priest G. (2005) Towards non-being. Clarendon Press, OxfordGoogle Scholar
  40. Quine W. (1960) Word and object. MIT Press, Cambridge, MassGoogle Scholar
  41. Sloman A., Logan B. (1999) Building cognitively rich agents using the SIM AGENT toolkit. Communications of the ACM 42(3): 71–77CrossRefGoogle Scholar
  42. Stalnaker R. (1991) The problem of logical omniscience I. Synthese 89: 425–440CrossRefGoogle Scholar
  43. Stich S. (1983) From folk psychology to cognitive science. MIT press, Cambridge, MassGoogle Scholar
  44. Thomason R. (1980) A note on syntactical treatments of modality. Synthese 44: 391–395CrossRefGoogle Scholar
  45. 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.
  46. van Ditmarsch, H., van der Hoek, W., & Kooi, B. (2007). Dynamic epistemic logic, Vol. 337 of Synthese Library. Springer.Google Scholar
  47. Vianu V. (1997) Rule-based languages. Annals of Mathematics and Artificial Intelligence 19: 215–259CrossRefGoogle Scholar
  48. 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.Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  1. 1.Department of PhilosophyMacquarie UniversitySydneyAustralia

Personalised recommendations