Focused most probable world computations in probabilistic logic programs

The “Most Probable World” (MPW) problem in probabilistic logic programming (PLPs) is that of finding a possible world with the highest probability. Past work has shown that this problem is computationally intractable and involves solving exponentially many linear programs, each of which is of exponential size. In this paper, we study what happens when the user focuses his interest on a set of atoms in such a PLP. We show that we can significantly reduce the number of worlds to be considered by defining a “reduced” linear program whose solution is in one-one correspondence with the exact solution to the MPW problem. However, the problem is still intractable. We develop a Monte Carlo sampling approach that enables us to build a quick approximation of the reduced linear program that allows us to estimate (inexactly) the solution to the MPW problem. We show experimentally that our approach works well in practice, scaling well to problems where the exact solution is intractable to compute.

[1]  Ehud Y. Shapiro,et al.  Logic Programs With Uncertainties: A Tool for Implementing Rule-Based Systems , 1983, IJCAI.

[2]  J. Lloyd.  Foundations of Logic Programming , 1984, Symbolic Computation.

[3]  Avi Wigderson,et al.  Pairwise Independence and Derandomization , 2006, Found. Trends Theor. Comput. Sci..

[4]  V. S. Subrahmanian,et al.  A semantical framework for supporting subjective and conditional probabilities in deductive databases , 1990, Journal of Automated Reasoning.

[5]  Torsten Schaub,et al.  COBA 2.0: A Consistency-Based Belief Change System , 2007, ECSQARU.

[6]  Gai CarSO.  A Logic for Reasoning about Probabilities * , 2004 .

[7]  V. S. Subrahmanian,et al.  The SOMA Terror Organization Portal (STOP): social network and analytic tools for the real-time analysis of terror groups , 2008 .

[8]  Samir Khuller,et al.  Finding Most Probable Worlds of Probabilistic Logic Programs , 2007, SUM.

[9]  V. S. Subrahmanian,et al.  Stochastic Opponent Modeling Agents: A Case Study with Hezbollah , 2008 .

[10]  Laks V. S. Lakshmanan,et al.  A Parametric Approach to Deductive Databases with Uncertainty , 1996, Logic in Databases.

[11]  Joseph Y. Halpern.  An Analysis of First-Order Logics of Probability , 1989, IJCAI.

[12]  Weiru Liu,et al.  Measuring the Ignorance and Degree of Satisfaction for Answering Queries in Imprecise Probabilistic Logic Programs , 2008, SUM.

[13]  Gabriele Kern-Isbernery.  Probabilistic Logic Programming under Maximum Entropy Justus-liebig- Universit at Gieeen Ifig Research Report Probabilistic Logic Programming under Maximum Entropy , 1999 .

[14]  Peter Haddawy,et al.  Probabilistic Logic Programming and Bayesian Networks , 1995, ASIAN.

[15]  V. S. Subrahmanian,et al.  Heterogeneous Active Agents, I: Semantics , 1999, Artif. Intell..

[16]  S. Shankar Sastry,et al.  Tracking on a graph , 2005, IPSN 2005. Fourth International Symposium on Information Processing in Sensor Networks, 2005..

[17]  Hector J. Levesque,et al.  A New Method for Solving Hard Satisfiability Problems , 1992, AAAI.

[18]  Thomas Lukasiewicz,et al.  Probabilistic Logic Programming , 1998, ECAI.

[19]  V. S. Subrahmanian,et al.  Optimal models of disjunctive logic programs: semantics, complexity, and computation , 2004, IEEE Transactions on Knowledge and Data Engineering.

[20]  Bart Selman,et al.  Accelerating Random Walks , 2002, CP.

[21]  U. Schöning.  A probabilistic algorithm for k-SAT and constraint satisfaction problems , 1999, 40th Annual Symposium on Foundations of Computer Science (Cat. No.99CB37039).

[22]  John Wylie Lloyd,et al.  Foundations of Logic Programming , 1987, Symbolic Computation.

[23]  Theodore Hailperin,et al.  Probability logic , 1984, Notre Dame J. Formal Log..

[24]  V. S. Subrahmanian,et al.  Hybrid Probabilistic Programs , 2000, J. Log. Program..

[25]  V. S. Subrahmanian,et al.  Stochastic Opponent Modeling Agents : A Case Study with Hamas , 2008 .

[26]  V. S. Subrahmanian,et al.  Optimal status sets of heterogeneous agent programs , 2005, AAMAS '05.

[27]  M. H. van Emden,et al.  Quantitative Deduction and its Fixpoint Theory , 1986, J. Log. Program..

[28]  Luís Moniz Pereira,et al.  Coherent Well-founded Annotated Logic Programs , 1999, LPNMR.

[29]  Nils J. Nilsson,et al.  Probabilistic Logic * , 2022 .

[30]  V. S. Subrahmanian,et al.  A stochastic language for modelling opponent agents , 2006, AAMAS '06.

[31]  Samir Khuller,et al.  Computing most probable worlds of action probabilistic logic programs: scalable estimation for 1030,000 worlds , 2007, Annals of Mathematics and Artificial Intelligence.

[32]  Ravi Montenegro,et al.  Mathematical Aspects of Mixing Times in Markov Chains , 2006, Found. Trends Theor. Comput. Sci..

[33]  Pierre Hansen,et al.  Column Generation Methods for Probabilistic Logic , 1989, INFORMS J. Comput..

[34]  A. Sliva,et al.  SOMA Models of the Behaviors of Stakeholders in the Afghan Drug Economy: A Preliminary Report , 2007 .

[35]  Laks V. S. Lakshmanan,et al.  ProbView: a flexible probabilistic database system , 1997, TODS.

[36]  J. W. Lloyd,et al.  Foundations of logic programming; (2nd extended ed.) , 1987 .

[37]  Bart Selman,et al.  Noise Strategies for Improving Local Search , 1994, AAAI.

[38]  Michael J. Black,et al.  A Probabilistic Framework for Matching Temporal Trajectories: CONDENSATION-Based Recognition of Gestures and Expressions , 1998, ECCV.

[39]  C.H. Papadimitriou,et al.  On selecting a satisfying truth assignment , 1991, [1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science.