Towards the Computation of Stable Probabilistic Model Semantics

In [22], a stable model semantics extension of the language of hybrid probabilistic logic programs [21] with non-monotonic negation, normal hybrid probabilistic programs (NHPP), has been developed by introducing the notion of stable probabilistic model semantics. It has been shown in [22] that the stable probabilistic model semantics is a natural extension of the stable model semantics for normal logic programs and the language of normal logic programs is a subset of the language NHPP. This suggests that efficient algorithms and implementations for computing the stable probabilistic model semantics for NHPP can be developed by extending the efficient algorithms and implementation for computing the stable model semantics for normal logic programs, e.g., SMODELS [17]. In this paper, we explore an algorithm for computing the stable probabilistic model semantics for NHPP along with its auxiliary functions. The algorithm we develop is based on the SMODELS [17] algorithms. We show the soundness and completeness of the proposed algorithm. We provide the necessary conditions that these auxiliary functions have to satisfy to guarantee the soundness and completeness of the proposed algorithm. This algorithm is the first to develop for studying computational methods for computing the stable probabilistic models semantics for hybrid probabilistic logic programs with non-monotonic negation.

[1]  Enrico Pontelli,et al.  Hybrid probabilistic programs with non-monotonic negation: semantics and algorithms , 2005 .

[2]  Anil Nerode,et al.  Mixed integer programming methods for computing nonmonotonic deductive databases , 1994, JACM.

[3]  Allen Van Gelder,et al.  The Alternating Fixpoint of Logic Programs with Negation , 1993, J. Comput. Syst. Sci..

[4]  V. S. Subrahmanian,et al.  Hybrid Probabilistic Programs: Algorithms and Complexity , 1999, UAI.

[5]  V. S. Subrahmanian,et al.  Probabilistic Logic Programming , 1992, Inf. Comput..

[6]  Krzysztof R. Apt,et al.  Logic Programming , 1990, Handbook of Theoretical Computer Science, Volume B: Formal Models and Sematics.

[7]  Enrico Pontelli,et al.  Towards a More Practical Hybrid Probabilistic Logic Programming Framework , 2005, PADL.

[8]  Laks V. S. Lakshmanan,et al.  On a theory of probabilistic deductive databases , 2001, Theory and Practice of Logic Programming.

[9]  James J. Lu,et al.  Computing Annotated Logic Programs , 1994, ICLP.

[10]  Ilkka Niemelä,et al.  Stable Model Semantics of Weight Constraint Rules , 1999, LPNMR.

[11]  Victor W. Marek,et al.  Computing with Default Logic , 1999, Artif. Intell..

[12]  Ilkka Niemelä,et al.  Efficient Implementation of the Well-founded and Stable Model Semantics , 1996, JICSLP.

[13]  V. Lifschitz,et al.  Foundations of Logic Programming , 1997 .

[14]  Maurice Bruynooghe,et al.  Logic programs with annotated disjunctions , 2004, NMR.

[15]  V. S. Subrahmanian,et al.  WFS + Branch and Bound = Stable Models , 1995, IEEE Trans. Knowl. Data Eng..

[16]  Jean H. Gallier,et al.  Linear-Time Algorithms for Testing the Satisfiability of Propositional Horn Formulae , 1984, J. Log. Program..

[17]  David Scott Warren,et al.  Computation of Stable Models and Its Integration with Logical Query Processing , 1996, IEEE Trans. Knowl. Data Eng..

[18]  G. Brewka.  Principles of Knowledge Representation , 1996 .

[19]  Enrico Pontelli,et al.  Hybrid Probabilistic Logic Programs with Non-monotonic Negation , 2005, ICLP.

[20]  Victor W. Marek,et al.  Autoepistemic logic , 1991, JACM.

[21]  Kenneth A. Ross,et al.  The well-founded semantics for general logic programs , 1991, JACM.

[22]  V. S. Subrahmanian,et al.  Stable Semantics for Probabilistic Deductive Databases , 1994, Inf. Comput..

[23]  Raymond Reiter,et al.  A Logic for Default Reasoning , 1987, Artif. Intell..

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