Title: Non-Incremental Bottom-Up Knowledge Compilation of Neuro-Answer Set Programs
Primary area: neurosymbolic & hybrid AI systems (physics-informed, logic & formal reasoning, etc.)
Keywords: Probabilistic Logic Programming, Knowledge Compilation

Abstract: Neuro-Probabilistic Answer Set Programming offers an intuitive and expressive framework for representing knowledge involving relations, non-determinism, logical constraints, and uncertainty-aware perception. Such a high expressivity comes at a significant computational cost. To mitigate that, Knowledge Compilation (KC) approaches translate the logic program into a logic circuit for which  inference and learning can be performed efficiently. Top-down KC approaches employ an intermediary step of translating the logic program into a CNF propositional formula, before the actual KC step. This has the drawback of requiring the use of auxiliary variables and a fixed variable ordering. Bottom-up KC approaches instead construct a circuit representation compositionally, by employing circuit operations that represent the subparts of the logic program, without the need of auxiliary variables and allowing dynamic variable ordering. However, intermediary circuits can grow quite large even when the end circuit is succinct. In this work, we develop a non-incremental bottom-up KC strategy that provably and empirically reduces the size of the intermediary representations compared to its incremental counterpart. We explore heuristics for v-tree initialization and dynamic variable reordering. Experimental results show that our method achieves state-of-the-art performance for a large class of programs.

TL;DR: We propose a non-incremental approach for Bottom-Up Knowledge Compilation of Probabilistic Answer Set programs.