Skip to main content

Logic, Knowledge Representation, and Bayesian Decision Theory

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 1861))

Abstract

In this paper I give a brief overview of recent work on uncertainty in AI, and relate it to logical representations. Bayesian decision theory and logic are both normative frameworks for reasoning that emphasize different aspects of intelligent reasoning. Belief networks (Bayesian networks) are representations of independence that form the basis for understanding much of the recent work on reasoning under uncertainty, evidential and causal reasoning, decision analysis, dynamical systems, optimal control, reinforcement learning and Bayesian learning. The independent choice logic provides a bridge between logical representations and belief networks that lets us understand these other representations and their relationship to logic and shows how they can extended to first-order rule-based representations. This paper discusses what the representations of uncertainty can bring to the computational logic community and what the computational logic community can bring to those studying reasoning under uncertainty.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Apt, K. R. and Bezem, M. (1991). Acyclic programs, New Generation Computing 9(3–4): 335–363.

    Article  Google Scholar 

  • Bacchus, F., Halpern, J. Y. and Levesque, H. J. (1999). Reasoning about noisy sensors and effectors in the situation calculus, Artificial Intelligence 111(1–2): 171–208. http://www.lpaig.uwaterloo.ca/~fbacchus/on-line.html

    Article  MATH  MathSciNet  Google Scholar 

  • Bertsekas, D. P. (1995). Dynamic Programming and Optimal Control, Athena Scientific, Belmont, Massachusetts. Two volumes.

    MATH  Google Scholar 

  • Bertsekas, D. P. and Tsitsiklis, J. N. (1996). Neuro-Dynamic Programming, Athena Scientific, Belmont, Massachusetts.

    MATH  Google Scholar 

  • Boutilier, C., Dean, T. and Hanks, S. (1999). Decision-theoretic planning: Structual assumptions and computational leverage, Journal of Artificial Intelligence Research 11: 1–94.

    MATH  MathSciNet  Google Scholar 

  • Boutilier, C., Dearden, R. and Goldszmidt, M. (1995). Exploiting structure in policy construction, Proc. 14th International Joint Conf. on Artificial Intelligence (IJCAI-95), Montreal, Québec, pp. 1104–1111.

    Google Scholar 

  • Boutilier, C., Friedman, N., Goldszmidt, M. and Roller, D. (1996). Context-specific independence in Bayesian networks, in E. Horvitz and F. Jensen (eds), Proc. Twelfth Conf. on Uncertainty in Artificial Intelligence (UAI-96), Portland, OR, pp. 115–123.

    Google Scholar 

  • Buntine, W. L.(1994). Operations for learning with graphical models, Journal of Artificial Intelligence Research 2 159–225.

    Google Scholar 

  • Cassandra, A., Littman, M. and Zhang, N. (1997). Incermental pruning: A simple, fast, exact mehtod for partially observable markov decision processes, in D. Geiger and P. Shenoy (eds), Proc. Thirteenth Conf. on Uncertainty in Artificial Intelligence (UAI-97), pp.--–--

    Google Scholar 

  • Cassandra, A. R., Kaelbling, L. P. and Littman, M. L. (1994). Acting optimally in partially observable stochastic domains, Proc. 12th National Conference on Artificial Intelligence, Seattle, pp. 1023–1028.

    Google Scholar 

  • Chang, C. L. and Lee, R. C. T. (1973). Symbolic Logical and Mechanical Theorem Proving, Academic Press, New York.

    Google Scholar 

  • Chapman, D. and Kaelbling, L. P. (1991). Input generlization in delayed reinforcement learning: An algorithm and performance comparisons, Proc. 12th International Joint Conf. on Artificial Intelligence (IJCAI-91), Sydney, Australia.

    Google Scholar 

  • Chickering, D. M., Heckerman, D. and Meek, C. (1997). A bayesian approach to learning bayesian networks with local structure, Proc. Thirteenth Conf. on Uncertainty in Artificial Intelligence (UAI-97), pp. 80–89.

    Google Scholar 

  • Dagum, P. and Luby, M. (1997). An optimal approximation algorithm for Bayesian inference, Artificial Intelligence 93(1–2): 1–27.

    Article  MATH  MathSciNet  Google Scholar 

  • Dean, T. and Kanazawa, K. (1989). A model for reasoning about persistence and causation, Computational Intelligence 5(3): 142–150.

    Article  Google Scholar 

  • Dean, T. L. and Wellman, M. P. (1991). Planning and Control, Morgan Kaufmann, San Mateo, CA.

    Google Scholar 

  • Dechter, R. (1996). Bucket elimination: A unifying framework for probabilistic inference, in E. Horvitz and F. Jensen (eds), Proc. Twelfth Conf. on Uncertainty in Artificial Intelligence (UAI-96), Portland, OR, pp. 211–219.

    Google Scholar 

  • Fikes, R. E. and Nilsson, N. J. (1971). STRIPS: A new approach to the application of theorem proving to problem solving, Artificial Intelligence 2(3–4): 189–208.

    Article  MATH  Google Scholar 

  • Friedman, N. and Goldszmidt, M. (1996). Learning Bayesian networks with local structure, Proc. Twelfth Conf. on Uncertainty in Artificial Intelligence (UAI-96), pp. 252–262. http://www2.sis.pitt.edu/~dsl/UAI/UAI96/Friedman1.UAI96.html

  • Fudenberg, D. and Tirole, J. (1992). Game Theory, MIT Press, Cambridge, MA.

    Google Scholar 

  • Heckerman, D. (1995). A tutorial on learning with Bayesian networks, Technical Report MSR-TR-95-06, Microsoft Research. (Revised November 1996). http://www.research.microsoft.com/research/dtg/heekerma/heckerma.html

  • Henrion, M. (1988). Propagating uncertainty in Bayesian networks by probabilistic logic sampling, in J. F. Lemmer and L. N. Kanal (eds), Uncertainty in Artificial Intelligence 2, Elsevier Science Publishers B.V., pp. 149–163.

    Google Scholar 

  • Henrion, M., Breese, J. and Horvitz, E. (1991). Decision analysis and expert systems, AI Magazine 12(4): 61–94.

    Google Scholar 

  • Hobbs, J. R., Stickel, M. E., Appelt, D. E. and Martin, P. (1993). Interpretation as abduction, Artificial Intelligence 63(1–2): 69–142.

    Article  Google Scholar 

  • Horvitz, E. J. (1989). Reasoning about beliefs and actions under computational resource constraints, in L. Kanal, T. Levitt and J. Lemmer (eds), Uncertainty in Artificial Intelligence 3, Elsevier, New York, pp. 301–324.

    Google Scholar 

  • Howard, R. A. and Matheson, J. E. (1984). Influence diagrams, in R. A. Howard and J. E. Matheson (eds), The Principles and Applications of Decision Analysis, Strategic Decisions Group, Menlo Park, CA.

    Google Scholar 

  • Jensen, F. V. (1996). An Introduction to Bayesian Networks, Springer Verlag, New York.

    Google Scholar 

  • Jordan, M. I., Ghahramani, Z., Jaakkola, T. S. and Saul, L. K. (1997). An introduction to variational methods for graphical models, Technical report, MIT Computational Cognitive Science. http://www.ai.mit.edu/projects/jordan.html

  • Jurafsky, D. and Martin, J. (2000). Speech and Language Processing, Prentice Hall.

    Google Scholar 

  • Kaelbling, L. P., Littman, M. L. and Moore, A. W. (1996). Reinforcement learning: A survey, Journal of Artificial Intelligence Research 4: 237–285.

    Google Scholar 

  • Koller, D. and Megiddo, N. (1992). The complexity of two-person zero-sum games in extensive form, Games and Economic Behavior 4: 528–552.

    Article  MATH  MathSciNet  Google Scholar 

  • Lauritzen, S. L. and Spiegelhalter, D. J. (1988). Local computations with probabilities on graphical structures and their application to expert systems, Journal of the Royal Statistical Society, Series 50(2): 157–224.

    MATH  MathSciNet  Google Scholar 

  • Lloyd, J. W. (1987). Foundations of Logic Programming, Symbolic Computation Series, second edn, Springer-Verlag, Berlin.

    MATH  Google Scholar 

  • Luenberger, D. G.(1979). Introduction to Dynamic Systems: Theory, Models and Applications, Wiley, New York.

    MATH  Google Scholar 

  • McCarthy, J. and Hayes, P. J. (1969). Some philosophical problems from the standpoint of artificial intelligence, in M. Meltzer and D. Michie (eds), Machine Intelligence 4, Edinburgh University Press, pp. 463–502.

    Google Scholar 

  • Muggleton, S. (1995). Inverse entailment and Progol, New Generation Computing 13(3,4): 245–286.

    Google Scholar 

  • Muggleton, S. and De Raedt, L. (1994). Inductive logic programming: Theory and methods, Journal of Logic Programming 19, 20: 629–679.

    Article  MathSciNet  Google Scholar 

  • Myerson, R. B. (1991). Game Theory: Analysis of Conflict, Harvard University Press, Cambridge, MA.

    MATH  Google Scholar 

  • Nilsson, N. J. (1991). Logic and artificial intelligence, Artificial Intelligence 47: 31–56.

    Article  MathSciNet  Google Scholar 

  • Ordeshook, P. C. (1986). Game theory and political theory: An introduction, Cambridge University Press, New York.

    Google Scholar 

  • Pearl, J. (1987). Evidential reasoning using stochastic simulation of causal models, Artificial Intelligence 32(2): 245–257.

    Article  MATH  MathSciNet  Google Scholar 

  • Pearl, J. (1988). Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference, Morgan Kaufmann, San Mateo, CA.

    Google Scholar 

  • Pearl, J. (1999). Reasoning with cause and effect, Proc. 16th International Joint Conf. on Artificial Intelligence (IJCAI-99), pp. 1437–1449.

    Google Scholar 

  • Pearl, J. (2000). Causality: Models, Reasoning and Inference, Cambridge University Press.

    Google Scholar 

  • Poole, D. (1989). Explanation and prediction: An architecture for default and abductive reasoning, Computational Intelligence 5(2): 97–110.

    Article  MathSciNet  Google Scholar 

  • Poole, D. (1990). A methodology for using a default and abductive reasoning system, International Journal of Intelligent Systems 5(5): 521–548.

    Article  MATH  MathSciNet  Google Scholar 

  • Poole, D. (1991a). Representing diagnostic knowledge for probabilistic Horn abduction, Proc. 12th International Joint Conf. on Artificial Intelligence (IJCAI-91), Sydney, pp. 1129–1135.

    Google Scholar 

  • Poole, D. (1991b). Search-based implementations of probabilistic Horn abduction, Technical report, Department of Computer Science, University of British Columbia, Vancouver, B.C., Canada.

    Google Scholar 

  • Poole, D.(1993a). Logic programming, abduction and probability: A top-down anytime algorithm for computing prior and posterior probabilities, New Generation Computing 11(3–4): 377–400.

    Google Scholar 

  • Poole, D. (1993b). Probabilistic Horn abduction and Bayesian networks, Artificial Intelligence 64(1): 81–129.

    Article  MATH  Google Scholar 

  • Poole, D. (1996a). Probabilistic conflicts in a search algorithm for estimating posterior probabilities in Bayesian networks, Artificial Intelligence 88: 69–100.

    Article  MATH  Google Scholar 

  • Poole, D. (1996b). Probabilistic conflicts in a search algorithm for estimating posterior probabilities in Bayesian networks, Artificial Intelligence 88: 69–100.

    Article  MATH  Google Scholar 

  • Poole, D. (1997a). The independent choice logic for modelling multiple agents under uncertainty, Artificial Intelligence 94: 7–56. special issue on economic principles of multi-agent systems. http://www.s.ube.ca/spider/poole/abstraets/icl.html

    Article  MATH  MathSciNet  Google Scholar 

  • Poole, D. (1997b). Probabilistic partial evaluation: Exploiting rule structure in probabilistic inference, Proc. 15th International Joint Conf. on Artificial Intelligence (IJCAI-97), Nagoya, Japan, pp. 1284–1291. http://www.s.ube.ca/spider/poole/abstraets/pro-pa.html

  • Poole, D. (1998). Decision theory, the situation calculus and conditional plans, Electronic Transactions on Artificial Intelligence 2(1–2). http://www.etaij.org

  • Poole, D. (2000a). Abducing through negation as failure: stable models in the Independent Choice Logic, Journal of Logic Programming 44(1–3): 5–35. http://www.s.ube.ca/spider/poole/abstracts/abnaf.html

    Article  MATH  MathSciNet  Google Scholar 

  • Poole, D. (2000b). Learning, bayesian probability, graphical models, and abduction, in P. Flach and A. Kakas (eds), Abduction and Induction: essays on their relation and integration, Kluwer.

    Google Scholar 

  • Poole, D., Mackworth, A. and Goebel, R. (1998). Computational Intelligence: A Logical Approach, Oxford University Press, New York.

    MATH  Google Scholar 

  • Quinlan, J. R. and Cameron-Jones, R. M. (1995). Induction of logic programs: FOIL and related systems, New Generation Computing 13(3,4): 287–312.

    Google Scholar 

  • Rabiner, L. (1989). A tutorial on hidden Markov models and selected applications in speech recognition, Proceedings of the IEEE 77(2): 257–286.

    Article  Google Scholar 

  • Russell, S. (1997). Rationality and intelligence, Artificial Intelligence 94: 57–77.

    Article  MATH  Google Scholar 

  • Russell, S. J. and Subramanian, D. (1995). Provably bounded-optimal agents, Journal of Artificial Intelligence Research 2: 575–609.

    MATH  Google Scholar 

  • Savage, L. J. (1972). The Foundation of Statistics, 2nd edn, Dover, New York.

    Google Scholar 

  • Shanahan, M. (1989). Prediction is deduction, but explanation is abduction, Proc. 11th International Joint Conf. on Artificial Intelligence (IJCAI-89), Detroit, MI, pp. 1055–1060.

    Google Scholar 

  • Shanahan, M.(1997). Solving the Frame Problem: A Mathematical Investigation of the Common Sense Law of Inertia, MIT Press, Cambridge, MA.

    Google Scholar 

  • Simon, H. (1996). The Sciences of the Artificial, third edn, MIT Press, Cambridge, MA.

    Google Scholar 

  • Sutton, R. S. and Barto, A. G. (1998). Reinforcement Learning: An Introduction, MIT Press, Canbridge, MA.

    Google Scholar 

  • Von Neumann, J. and Morgenstern, (1953). Theory of Games and Economic Behavior, third edn, Princeton University Press, Princeton, NJ.

    MATH  Google Scholar 

  • Zhang, N. and Poole, D. (1996). Exploiting causal independence in Bayesian network inference, Journal of Artificial Intelligence Research 5: 301–328.

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2000 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Poole, D. (2000). Logic, Knowledge Representation, and Bayesian Decision Theory. In: Lloyd, J., et al. Computational Logic — CL 2000. CL 2000. Lecture Notes in Computer Science(), vol 1861. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44957-4_5

Download citation

  • DOI: https://doi.org/10.1007/3-540-44957-4_5

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-67797-0

  • Online ISBN: 978-3-540-44957-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics