Constraint Propagation for Efficient Inference in Markov Logic

Abstract

Many real world problems can be modeled using a combination of hard and soft constraints. Markov Logic is a highly expressive language which represents the underlying constraints by attaching realvalued weights to formulas in first order logic. The weight of a formula represents the strength of the corresponding constraint. Hard constraints are represented as formulas with infinite weight. The theory is compiled into a ground Markov network over which probabilistic inference can be done. For many problems, hard constraints pose a significant challenge to the probabilistic inference engine. However, solving the hard constraints (partially or fully) before hand outside of the probabilistic engine can hugely simplify the ground Markov network and speed probabilistic inference. In this work, we propose a generalized arc consistency algorithm that prunes the domains of predicates by propagating hard constraints. Our algorithm effectively performs unit propagation at a lifted level, avoiding the need to explicitly ground the hard constraints during the pre-processing phase, yielding a potentially exponential savings in space and time. Our approach results in much simplified domains, thereby, making the inference significantly more efficient both in terms of time and memory. Experimental evaluation over one artificial and two real-world datasets show the benefit of our approach.