Constraint-Based Inference in Probabilistic Logic Programs

Abstract

Probabilistic Logic Programs (PLPs) generalize traditional logic programs and allow the encoding of models combining logical structure and uncertainty. In PLP, inference is performed by summarizing the possible worlds which entail the query in a suitable data structure, and using it to compute the answer probability. Systems such as ProbLog, PITA, etc., use propositional data structures like explanation graphs, BDDs, SDDs, etc., to represent the possible worlds. While this approach saves inference time due to substructure sharing, there are a number of problems where a more compact data structure is possible. We propose a data structure called Ordered Symbolic Derivation Diagram (OSDD) which captures the possible worlds by means of constraint formulas. We describe a program transformation technique to construct OSDDs via query evaluation, and give procedures to perform exact and approximate inference over OSDDs. Our approach has two key properties. Firstly, the exact inference procedure is a generalization of traditional inference, and results in speedup over the latter in certain settings. Secondly, the approximate technique is a generalization of likelihood weighting in Bayesian Networks, and allows us to perform sampling-based inference with lower rejection rate and variance. We evaluate the effectiveness of the proposed techniques through experiments on several problems. This paper is under consideration for acceptance in TPLP.Definition 2 (Constraint Graph). The constraint graph for a constraint formula γ is labeled undirected graph, whose nodes are variables and ground terms in γ. Edges are labeled with "=" and " =" such that • T 1 and T 2 are connected by an edge labeled "=" if, and only if, T 1 = T 2 is entailed by γ.• T 1 and T 2 are connected by an edge labeled " =" if, and only if, T 1 = T 2 is entailed by γ, and at least one of T 1 , T 2 is a variable.

Implementing a Library for Probabilistic Programming Using Non-strict Non-determinism

“…After presenting the basic combinators of the library and motivating the advantages of modeling distributions using non-determinism, we will implement some exemplary applications. We reimplement examples that have been characterized as challenging for probabilistic logic programming by Nampally and Ramakrishnan (Nampally and Ramakrishnan 2015), who use the examples to discuss the expressiveness of probabilistic logic programming and its cost with respect to performance. The examples focus on properties of random strings and their probabilities.…”