Sampling-Based SAT/ASP Multi-model Optimization as a Framework for Probabilistic Inference

This paper proposes multi-model optimization through SAT witness or answer set sampling, with common probabilistic reasoning tasks as primary use cases (including deduction-style probabilistic inference and hypothesis weight learning). Our approach enhances a state-of-the-art SAT/ASP solving algorithm with Gradient Descent as branching literal decision approach, and optionally a cost backtracking mechanism. Sampling of models using these methods minimizes a task-specific, user-provided multi-model cost function while adhering to given logical background knowledge (either a Boolean formula in CNF or a normal logic program under stable model semantics). Features of the framework include its relative simplicity and high degree of expressiveness, since arbitrary differentiable cost functions and background knowledge can be provided.