Gerardo I. Simari
John P. Dickerson
Abstract
Action-probabilistic logic programs (ap-programs) are a class of probabilistic logic programs that have been extensively used during the last few years for modeling behaviors of entities. Rules in ap-programs have the form “If the environment in which entity E operates satisfies certain conditions, then the probability that E will take some action A is between L and U”. Given an ap-program, we are interested in trying to change the environment, subject to some constraints, so that the probability that entity E takes some action (or combination of actions) is maximized. This is called the Basic Abductive Query Answering Problem (BAQA). We first formally define and study the complexity of BAQA, and then go on to provide an exact (exponential time) algorithm to solve it, followed by more efficient algorithms for specific subclasses of the problem. We also develop appropriate heuristics to solve BAQA efficiently.
The second problem, called the Cost-based Query Answering (CBQA) problem checks to see if there is some way of achieving a desired action (or set of actions) with a probability exceeding a threshold, given certain costs. We first formally define and study an exact (intractable) approach to CBQA, and then go on to propose a more efficient algorithm for a specific subclass of ap-programs that builds on the results for the basic version of this problem. We also develop the first algorithms for parallel evaluation of CBQA. We conclude with an extensive report on experimental evaluations performed over prototype implementations of the algorithms developed for both BAQA and CBQA, showing that our parallel algorithms work well in practice.
- Asal, V., Carter, J., and Wilkenfeld, J. 2008. Ethnopolitical violence and terrorism in the Middle East. In Peace and Conflict 2008, J. Hewitt, J. Wilkenfeld, and T. Gurr Eds., Paradigm.Google Scholar
- Baldoni, M., Giordano, L., Martelli, A., and Patti, V. 1997. An abductive proof procedure for reasoning about actions in modal logic programming. In Selected Papers from the Workshop on Non-Monotonic Extensions of Logic Programming (NMELP’96). Springer, 132--150. Google ScholarDigital Library
- Bellman, R. 1957. A Markovian decision process. J. Math. Mech. 6.Google Scholar
- Bhatnagar, R. and Kanal, L. 1993. Structural and probabilistic knowledge for abductive reasoning. IEEE Trans. Pattern Anal. Mach. Intell. 15, 3, 233--245. Google ScholarDigital Library
- Boutilier, C., Dearden, R., and Goldszmidt, M. 2000. Stochastic dynamic programming with factored representations. Artif. Intell. 121, 1--2, 49--107. Google ScholarDigital Library
- Bryson, J. J., Ando, Y., and Lehmann, H. 2007. Agent-based modelling as scientific method: A case study analysing primate social behaviour. Philos. Trans. R. Soc. London, Ser. B 362, 1485, 1685--1698.Google ScholarCross Ref
- Christiansen, H. 2008. Implementing probabilistic abductive logic programming with constraint handling rules. In Constraint Handling Rules, T. Schrijvers and T. W. Frühwirth Eds., Lecture Notes in Computer Science Series, vol. 5388, Springer, 85--118. Google ScholarDigital Library
- Chvtal, V. 1983. Linear Programming. W.H.Freeman, New York.Google Scholar
- Console, L. and Torasso, P. 1991. A spectrum of logical definitions of model-based diagnosis. Comput. Intell. 7, 3, 133--141 . Google ScholarDigital Library
- Cooper, G. and Herskovits, E. 1992. A Bayesian method for the induction of probabilistic networks from data. Machine Learning 9, 4, 309--347. Google ScholarDigital Library
- de Bonet, J. S., Isbell, C. L. Jr., and Viola, P. A. 1996. MIMIC: Finding optima by estimating probability densities. In Proceedings of the Conference on Advances in Neural Information Processing Systems (NIPS’96). MIT Press, 424--430.Google Scholar
- Denecker, M. and Kakas, A. C. 2002. Abduction in logic programming. In Computational Logic: Logic Programming and Beyond, Essays in Honour of Robert A. Kowalski, Part I, Springer, 402--436. Google ScholarDigital Library
- Eiter, T. and Gottlob, G. 1995. The complexity of logic-based abduction. J. ACM 42, 1, 3--42. Google ScholarDigital Library
- Eiter, T., Gottlob, G., and Leone, N. 1997a. Abduction from logic programs: Semantics and complexity. Theor. Comput. Sci. 189, 1--2, 129--177. Google ScholarDigital Library
- Eiter, T., Gottlob, G., and Leone, N. 1997b. Semantics and complexity of abduction from default theories. Artif. Intell. 90, 90--1. Google ScholarDigital Library
- Eshghi, K. 1988. Abductive planning with event calculus. In Proceedings of the International Conference on Logic Programming. 562--579.Google Scholar
- Fagin, R., Halpern, J. Y., and Megiddo, N. 1990. A logic for reasoning about probabilities. Inf. Comput. 87, 1/2, 78--128. Google ScholarDigital Library
- Giles, J. 2008. Can conflict forecasts predict violence hotspots? New Scientist 2647.Google Scholar
- Hailperin, T. 1984. Probability logic. Notre Dame Journal of Formal Logic 25, 3, 198--212.Google ScholarCross Ref
- Hall, M., Frank, E., Holmes, G., Pfahringer, B., Reutemann, P., and Witten, I. 2009. The WEKA data mining software: An update. ACM SIGKDD Explor. Newsletter 11, 1, 10--18. Google ScholarDigital Library
- Josang, A. 2008. Abductive reasoning with uncertainty. In Proceedings of the Conference on Information Processing and Management of Uncertainty, L. Magdalena, M. Ojeda-Aciego, and J. L. Verdegay Eds., 9--16.Google Scholar
- Kakas, A., Michael, A., and Mourlas, C. 2000. ACLP: Abductive constraint logic programming. J. Logic Program. 44, 129--177(49).Google ScholarCross Ref
- Kern-Isberner, G. and Lukasiewicz, T. 2004. Combining probabilistic logic programming with the power of maximum entropy. Artif. Intell. 157, 1--2, 139--202. Google ScholarDigital Library
- Khuller, S., Martinez, M. V., Nau, D. S., Sliva, A., Simari, G. I., and Subrahmanian, V. S. 2007. Computing most probable worlds of action probabilistic logic programs: Scalable estimation for 10 30,000 worlds. Ann. Math. Artif. Intell. 51, 2--4, 295--331. Google ScholarDigital Library
- Kohlas, J., Berzati, D., and Haenni, R. 2002. Probabilistic argumentation systems and abduction. Ann. Math. Artif. Intell. 34, 1--3, 177--195. Google ScholarDigital Library
- Littman, M. L. 1996. Algorithms for sequential decision making. Ph.D. thesis, Department of Computer Science, Brown University, Providence, RI. Google ScholarDigital Library
- Lloyd, J. W. 1987. Foundations of Logic Programming 2nd Ed. Springer. Google ScholarDigital Library
- Mannes, A., Michael, M., Pate, A., Sliva, A., Subrahmanian, V. S., and Wilkenfeld, J. 2008a. Stochastic opponent modeling agents: A case study with Hamas. In Proceedings of the International Conference on Computer and Communication Devices.Google Scholar
- Mannes, A., Michael, M., Pate, A., Sliva, A., Subrahmanian, V. S., and Wilkenfeld, J. 2008b. Stochastic opponent modelling agents: A case study with Hezbollah. In Proceedings of the 1st International Workshop on Social Computing, Behavioral Modeling, and Prediction. H. Liu and J. Salerno Eds.Google Scholar
- Ng, R. T. and Subrahmanian, V. S. 1992. Probabilistic logic programming. Inf. Comput. 101, 2, 150--201. Google ScholarDigital Library
- Ng, R. T. and Subrahmanian, V. S. 1993. A semantical framework for supporting subjective and conditional probabilities in deductive databases. J. Autom. Reason. 10, 2, 191--235.Google ScholarCross Ref
- Nilsson, N. 1986. Probabilistic logic. Artif. Intell. 28, 71--87. Google ScholarDigital Library
- Pearl, J. 1988. Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. Morgan Kaufmann Publishers Inc., San Francisco. Google ScholarDigital Library
- Pearl, J. 1991. Probabilistic and qualitative abduction. In Proceedings of the AAAI Spring Symposium on Abduction. AAAI Press, Stanford, CA, 155--158.Google Scholar
- Pelikan, M., Goldberg, D. E., and Lobo, F. G. 2002. A survey of optimization by building and using probabilistic models. Comput. Optim. Appl. 21, 1, 5--20. Google ScholarDigital Library
- Peng, Y. and Reggia, J. A. 1990. Abductive Inference Models for Diagnostic Problem-Solving. Springer. Google ScholarDigital Library
- Poole, D. 1993. Probabilistic Horn abduction and Bayesian networks. Artif. Intell. 64, 1, 81--129. Google ScholarDigital Library
- Poole, D. 1997. The independent choice logic for modelling multiple agents under uncertainty. Artif. Intell. 94, 1--2, 7--56. Google ScholarDigital Library
- Puterman, M. 1994. Markov Decision Processes: Discrete Stochastic Dynamic Programming. John Wiley & Sons. Google ScholarDigital Library
- Shanahan, M. 2000. An abductive event calculus planner. J. Logic Program. 44, 207--239.Google ScholarCross Ref
- Tseng, P. 1990. Solving H-horizon, stationary Markov decision problems in time proportional to log(H). Oper. Res. Lett. 9, 5, 287--297. Google ScholarDigital Library
- Tsitsiklis, J. and van Roy, B. 1996. Feature-based methods for large scale dynamic programming. Machine Learning 22, 1/2/3, 59--94. Google ScholarDigital Library
- Williams, R. and Baird, L. 1994. Tight performance bounds on greedy policies based on imperfect value functions. In Proceedings of the 10th Yale Workshop on Adaptive and Learning Systems.Google Scholar
Index Terms
- Parallel Abductive Query Answering in Probabilistic Logic Programs
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