Given a propositional formula ψ, the model counting problem, also referred to as #SAT, seeks to compute the number of satisfying assignments (or models) of ψ. Modern search-based model counting algorithms are built on conflict-driven clause learning, combined with the caching of certain subformulas (called components) encountered during the search process. Despite significant progress in these algorithms over the years, state-of-the-art model counters often struggle to handle large but structured instances that typically arise in combinatorial settings. Motivated by the observation that these counters do not exploit the inherent symmetries exhibited in such instances, we revisit the component caching architecture employed in current counters and introduce a novel caching scheme that focuses on identifying symmetric components. We first prove the soundness of our approach, and then integrate it into the state-of-the-art model counter GANAK. Our extensive experiments on hard combinatorial instances demonstrate that the resulting counter, SymGANAK, leads to improvements over GANAK both in terms of PAR-2 score and the number of instances solved.

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Recent advances in neural-symbolic learning, such as Deep-ProbLog, extend probabilistic logic programs with neural predicates. Like graphical models, these probabilistic logic programs define a probability distribution over possible worlds, for which inference is computationally hard. We propose Deep-StochLog, an alternative neural-symbolic framework based on stochastic definite clause grammars, a kind of stochastic logic program. More specifically, we introduce neural grammar rules into stochastic definite clause grammars to create a framework that can be trained end-to-end. We show that inference and learning in neural stochastic logic programming scale much better than for neural probabilistic logic programs. Furthermore, the experimental evaluation shows that DeepStochLog achieves state-of-the-art results on challenging neural-symbolic learning tasks.

An issue that has so far received only limited attention in probabilistic logic programming (PLP) is the modelling of so-called epistemic uncertainty, the uncertainty about the model itself. Accurately quantifying this model uncertainty is paramount to robust inference, learning and ultimately decision making. We introduce BetaProbLog, a PLP language that can model epistemic uncertainty. BetaProbLog has sound semantics, an effective inference algorithm that combines Monte Carlo techniques with knowledge compilation, and a parameter learning algorithm. We empirically outperform state-of-the-art methods on probabilistic inference tasks in second-order Bayesian networks, digit classification and discriminative learning in the presence of epistemic uncertainty.