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Abstract

Abstract. Stochastic logic programs (SLPs) are logic programs with parameterised clauses which define a loglinear distribution over refutations of goals. The log-linear distribution provides, by marginalisation, a distribution over variable bindings, allowing SLPs to compactly represent quite complex distributions.We analyse the fundamental statistical properties of SLPs addressing issues concerning infinite derivations, 'unnormalised' SLPs and impure SLPs. After detailing existing approaches to parameter estimation for log-linear models and their application to SLPs, we present a new algorithm called failure-adjusted maximisation (FAM). FAM is an instance of the EM algorithm that applies specifically to normalised SLPs and provides a closed-form for computing parameter updates within an iterative maximisation approach. We empirically show that FAM works on some small examples and discuss methods for applying it to bigger problems.

Logical Rule-Based Knowledge Graph Reasoning: A Comprehensive Survey

“…To enhance the efficiency of the inference tree, SLP [57] incorporates parameterized clauses and utilizes a logarithmic-linear distribution to invert the goal. SLP defines a stochastic process that traverses the SLD tree, where the probability distribution at each node is determined by assigning higher weights to the required answer clauses and lower weights to the other clauses.…”

Towards General Natural Language Understanding with Probabilistic Worldbuilding

“…PWM is certainly not the first to combine symbolic and probabilistic methods. There is a rich history of inductive logic programming (ILP) (Muggleton, 1991;Cropper and Morel, 2021) and probabilistic ILP languages (Muggleton, 1996;Cussens, 2001;Sato et al, 2005;Bellodi and Riguzzi, 2015). These languages could be used to learn a ''theory'' from a collection of observations, but they are typically restricted to learning rules in the form of first-order Horn clauses, for tractability.…”