A Modal Logic for the Decision-Theoretic Projection Problem

Gavin Rens, Thomas Meyer, Gerhard Lakemeyer

2015

Abstract

We present a decidable logic in which queries can be posed about (i) the degree of belief in a propositional sentence after an arbitrary finite number of actions and observations and (ii) the utility of a finite sequence of actions after a number of actions and observations. Another contribution of this work is that a POMDP model specification is allowed to be partial or incomplete with no restriction on the lack of information specified for the model. The model may even contain information about non-initial beliefs. Essentially, entailment of arbitrary queries (expressible in the language) can be answered. A sound, complete and terminating decision procedure is provided.

References

  1. Bacchus, F., Halpern, J., and Levesque, H. (1999). Reasoning about noisy sensors and effectors in the situation calculus. Artificial Intelligence, 111(1-2):171-208.
  2. Boutilier, C. and Poole, D. (1996). Computing optimal policies for partially observable decision processes using compact representations. In Proceedings of the Thirteenth National Conference on Artificial Intelligence (AAAI-96), pages 1168-1175, Menlo Park, CA. AAAI Press.
  3. Boutilier, C., Reiter, R., Soutchanski, M., and Thrun, S. (2000). Decision-theoretic, high-level agent programming in the situation calculus. In Proceedings of the Seventeenth National Conference on Artificial Intelligence (AAAI-00) and of the Twelfth Conference on Innovative Applications of Artificial Intelligence (IAAI00), pages 355-362. AAAI Press, Menlo Park, CA.
  4. De Weerdt, M., De Boer, F., Van der Hoek, W., and Meyer, J.-J. (1999). Imprecise observations of mobile robots specified by a modal logic. In Proceedings of the Fifth Annual Conference of the Advanced School for Computing and Imaging (ASCI-99), pages 184-190.
  5. Gabaldon, A. and Lakemeyer, G. (2007). E S P : A logic of only-knowing, noisy sensing and acting. In Proceedings of the Twenty-second National Conference on Artificial Intelligence (AAAI-07), pages 974-979. AAAI Press.
  6. Geffner, H. and Bonet, B. (1998). High-level planning and control with incomplete information using POMDPs. In Proceedings of the Fall AAAI Symposium on Cognitive Robotics, pages 113-120, Seattle, WA. AAAI Press.
  7. Hansen, E. and Feng, Z. (2000). Dynamic programming for POMDPs using a factored state representation. In Proceedings of the Fifth Intional Conference on Artificial Intelligence, Planning and Scheduling (AIPS-00), pages 130-139.
  8. Hansson, H. and Jonsson, B. (1994). A logic for reasoning about time and reliability. Formal Aspects of Computing, 6:512-535.
  9. Iocchi, L., Lukasiewicz, T., Nardi, D., and Rosati, R. (2009). Reasoning about actions with sensing under qualitative and probabilistic uncertainty. ACM Transactions on Computational Logic, 10(1):5:1-5:41.
  10. Kwiatkowska, M., Norman, G., and Parker, D. (2010). Advances and challenges of probabilistic model checking. In Proceedings of the Forty-eighth Annual Allerton Conference on Communication, Control and Computing, pages 1691-1698. IEEE Press.
  11. Levesque, H. and Lakemeyer, G. (2004). Situations, si! Situation terms no! In Proceedings of the Conference on Principles of Knowledge Representation and Reasoning (KR-04), pages 516-526. AAAI Press.
  12. Lison, P. (2010). Towards relational POMDPs for adaptive dialogue management. In Proceedings of the ACL 2010 Student Research Workshop, ACLstudent 7810, pages 7-12, Stroudsburg, PA, USA. Association for Computational Linguistics.
  13. Littman, M., Majercik, S., and Pitassi, T. (2001). Stochastic boolean satisfiability. Journal of Automated Reasoning, 27(3):251-296.
  14. McCarthy, J. (1963). Situations, actions and causal laws. Technical report, Stanford University.
  15. McCarthy, J. and Hayes, P. (1969). Some philosophical problems from the standpoint of artificial intelligence. Machine Intelligence, 4:463-502.
  16. Monahan, G. (1982). A survey of partially observable Markov decision processes: Theory, models, and algorithms. Management Science, 28(1):1-16.
  17. Poole, D. (1998). Decision theory, the situation calculus and conditional plans. Linköping Electronic Articles in Computer and Information Science, 8(3).
  18. Rens, G. (2014). Formalisms for Agents Reasoning with Stochastic Actions and Perceptions. PhD thesis, School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal.
  19. Rens, G., Meyer, T., and Lakemeyer, G. (2013). On the logical specification of probabilistic transition models. In Proceedings of the Eleventh International Symposium on Logical Formalizations of Commonsense Reasoning (COMMONSENSE 2013), University of Technology, Sydney. UTSe Press.
  20. Rens, G., Meyer, T., and Lakemeyer, G. (2014a). A logic for specifying stochastic actions and observations. In Beierle, C. and Meghini, C., editors, Proceedings of the Eighth International Symposium on Foundations of Information and Knowledge Systems (FoIKS), Lecture Notes in Computer Science, pages 305-323. Springer-Verlag.
  21. Rens, G., Meyer, T., and Lakemeyer, G. (2014b). SLAP: Specification logic of actions with probability. Journal of Applied Logic, 12(2):128-150.
  22. Ross, S., Pineau, J., Chaib-draa, B., and Kreitmann, P. (2011). A bayesian approach for learning and planning in partially observable markov decision processes. J. Mach. Learn. Res., 12:1729-1770.
  23. Saad, E. (2009). Probabilistic reasoning by sat solvers. In Sossai, C. and Chemello, G., editors, Proceedings of the Tenth European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty (ECSQARU-09), volume 5590 of Lecture Notes in Computer Science, pages 663-675, Berlin, Heidelberg. Springer-Verlag.
  24. Sanner, S. and Kersting, K. (2010). Symbolic dynamic programming for first-order POMDPs. In Proceedings of the Twenty-fourth National Conference on Artificial Intelligence (AAAI-10), pages 1140-1146. AAAI Press.
  25. Shirazi, A. and Amir, E. (2011). First-order logical filtering. Artificial Intelligence, 175(1):193-219.
  26. Smallwood, R. and Sondik, E. (1973). The optimal control of partially observable Markov processes over a finite horizon. Operations Research, 21:1071-1088.
  27. Wang, C., Joshi, S., and Khardon, R. (2008). First order decision diagrams for relational MDPs. Journal of Artificial Intelligence Research (JAIR), 31:431-472.
  28. Wang, C. and Khardon, R. (2010). Relational partially observable MDPs. In Fox, M. and Poole, D., editors, Proceedings of the Twenty-fourth AAAI Conference on Artificial Intelligence (AAAI-10). AAAI Press.
  29. Wang, C. and Schmolze, J. (2005). Planning with POMDPs using a compact, logic-based representation. In Proceedings of the Seventeenth IEEE International Conference on Tools with Artificial Intelligence (ICTAI05), pages 523-530, Los Alamitos, CA, USA. IEEE Computer Society.
Download


Paper Citation


in Harvard Style

Rens G., Meyer T. and Lakemeyer G. (2015). A Modal Logic for the Decision-Theoretic Projection Problem . In Proceedings of the International Conference on Agents and Artificial Intelligence - Volume 2: ICAART, ISBN 978-989-758-074-1, pages 5-16. DOI: 10.5220/0005168200050016


in Bibtex Style

@conference{icaart15,
author={Gavin Rens and Thomas Meyer and Gerhard Lakemeyer},
title={A Modal Logic for the Decision-Theoretic Projection Problem},
booktitle={Proceedings of the International Conference on Agents and Artificial Intelligence - Volume 2: ICAART,},
year={2015},
pages={5-16},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0005168200050016},
isbn={978-989-758-074-1},
}


in EndNote Style

TY - CONF
JO - Proceedings of the International Conference on Agents and Artificial Intelligence - Volume 2: ICAART,
TI - A Modal Logic for the Decision-Theoretic Projection Problem
SN - 978-989-758-074-1
AU - Rens G.
AU - Meyer T.
AU - Lakemeyer G.
PY - 2015
SP - 5
EP - 16
DO - 10.5220/0005168200050016