ILP-based Inference for Cost-based Abduction on First-order Predicate Logic

Abstract

Abduction is desirable for many natural language processing (NLP) tasks. While recent advances in large-scale knowledge acquisition warrant applying abduction with large knowledge bases to real-life NLP problems, as of yet, no existing approach to abduction has achieved the efficiency necessary to be a practical solution for largescale reasoning on real-life problems. In this paper, we propose an efficient solution for large-scale abduction. The contributions of our study are as follows: (i) we propose an efficient method of cost-based abduction in first-order predicate logic that avoids computationally expensive grounding procedures; (ii) we formulate the bestexplanation search problem as an integer linear programming optimization problem, making our approach extensible; (iii) we show how cutting plane inference, which is an iterative optimization strategy developed in operations research, can be applied to make abduction in first-order logic tractable; and (iv) the abductive inference engine presented in this paper is made publicly available.

Modeling Variations of First-Order Horn Abduction in Answer Set Programming

“…For experiments with Wa we follow existing practice (cf. [II13]) and set initial costs to ic(o) = 100$ for all o ∈ O and for each axiom we set weights to sum up to 1.2, i.e., we set w i = 1.2/r, 1 ≤ i ≤ r.…”

“…[ADLR15]. We also make experiments to compare with state-of-theart approaches Henry-n700 8 version 4b0d900 [II13] and its successor Phillip 9 version 5612b13 [YII + 15]. Each run was limited to 5 minutes and 5 GB RAM, HTCondor was used as a job scheduling system, each run was repeated 5 times and no more than 8 jobs were running simultaneously.…”

“…Due to its unfavorable performance, we omit results for Bwd-G in the following. The Henry-n700 solver realizes Wa and on the Accel benchmark results of around 10 sec per instance have been reported [II13]. Phillip is the successor of Henry-n700 and adds heuristics for a partial instantiation of the most relevant portions of the proof graph [YII + 15].…”

“…Several tools for realizing abduction with such preferences exist: Phillip, based on Integer Linear Programming (ILP) [YII + 15] and its precursor Henry-n700 [II13] as well as an approach based on Markov Logic [BHD + 11]. The problem of termination is solved in [BHD + 11] by instantiating existential terms only with terms from the input (no value invention), while [II13, YII + 15] solves the issue by inventing a new term only if no previously invented term is present in the head of the axiom.…”

“…• We apply a technique used to increase performance of the Henry-n700 solver [II13] for weighted abduction to our encodings by introducing on-demand constraints for transitivity of the equivalence relation and for ensuring acyclicity of the proof graph. We formalize this using HEX and describe an algorithm for computing optimal models in the presence of on-demand constraints using the Python API of Clingo [GKKS14] (Section 4.2).…”