Specialising Model Counting for Probabilistic Inference
(2025)
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- Abstract
- Reasoning under uncertainty is the task of reasoning about one or more uncertain events. Probability theory is the most common method for quantifying uncertainty. In this method, each event is represented by a random variable associated with a specific probability distribution. Probabilistic inference is the process of querying probabilistic models and has applications in many real-world domains, such as medicine, biology, weather prediction, and wildlife monitoring. Propositional logic has emerged over the last two decades as a method for solving probabilistic inference problems. In particular, computing the probability of some observation can be reduced to counting the number of satisfying assignments of a boolean formula; this is the weighted model counting (WMC) problem. Generally, the probabilistic inference tasks studied in this work and WMC are #P-Complete. Designing algorithms that solve such problems is challenging, but modern model counters efficiently solve a wide range of problems. However, such efficiency comes at the cost of complex solvers that are difficult to extend and modify. Nowadays, probabilistic logical reasoning solvers are used as a subtask in other AI domains; hence, it becomes crucial to have solvers that can be adapted to various contexts and requirements. This work explores how WMC can be specialised for probabilistic inference in a simple and easily adaptable manner. More specifically, we propose a new modelling language based on propositional logic that incorporates the structure of probabilistic models and a new solver that implements the most basic elements to solve the WMC problem. Moreover, we designed new algorithms to compute exact and approximate weighted model counts. A key contribution of our approximate method is a new way of computing an upper bound on the true weighted model count. Despite its simplicity, we demonstrate that this solver is competitive with state-of-the-art model counters and, in some cases, outperforms them.
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Citations
Dubray, A. (2025). Specialising Model Counting for Probabilistic Inference. https://hdl.handle.net/2078.5/246497