Using Iterative Deepening for Probabilistic Logic Inference

Abstract

We present a novel approach that uses an iterative deepening algorithm in order to perform probabilistic logic inference for ProbLog, a probabilistic extension of Prolog. The most used inference method for ProbLog is exact inference combined with tabling. Tabled exact inference first collects a set of SLG derivations which contain the probabilistic structure of the ProbLog program including the cycles. At a second step, inference requires handling these cycles in order to create a noncyclic Boolean representation of the probabilistic information. Finally, the Boolean representation is compiled to a data structure where inference can be performed in linear time. Previous work has illustrated that there are two limiting factors for ProbLog's exact inference. The first factor is the target compilation language and the second factor is the handling of the cycles. In this paper, we address the second factor by presenting an iterative deepening algorithm which handles cycles and produces solutions to problems that previously ProbLog was not able to solve. Our experimental results show that our iterative deepening approach gets approximate bounded values in almost all cases and in most cases we are able to get the exact result for the same or one lower scaling factor.

Probabilistic abstract argumentation frameworks, a possible world view

“…Programming that is closely related with PrAAFs. For efficient exact inference we direct the reader at [25,26,27,28,29], and for efficient approximate inference at [30,31,32].…”

“…MetaProbLog provides several different efficient probabilistic inference methods such as: (i) exact inference based on Reduced Ordered Binary Decision Diagrams (ROBDDs) and dynamic programming [25]; (ii) program (DAF) sampling with memoization [39]; (iii) any-time inference using an iterative deepening algorithm [40].…”

Generating Random Logic Programs Using Constraint Programming

“…Stratification is a condition necessary for probabilistic logic programs [18] and often enforced on logic programs [4] that helps to ensure a unique answer to every query. This is achieved by restricting the use of negation so that any program P can be partitioned into a sequence of programs P = n i=1 P i such that, for all i, the negative literals in P i can only refer to predicates defined in P j for j ≤ i [4].…”

Generating Random Logic Programs Using Constraint Programming

“…In this section, we present custom constraints for stratification and independence. Stratification is a condition necessary for probabilistic logic programs [18] and often enforced on logic programs [4] that helps to ensure a unique answer to every query, while independence is a fundamental concept in probability theory that imposes structure on the probability distribution and simplifies inference.…”