Title: Neurosymbolic Language Reasoning as Satisfiability Modulo Theory
Primary area: neurosymbolic & hybrid AI systems (physics-informed, logic & formal reasoning, etc.)
Keywords: neurosymbolic, SMT, logic, reasoning

Abstract: Natural language (NL) contains extensive logical structure, finely meshed with ''gestalt'' content best interpreted statistically. LLMs are indispensable for interpreting the gestalt content but known to perform unreliably on logic. We characterize this logical reasoning gap for traditional ``compositional'' tasks, but also for less appreciated "combinatorial'' tasks, that arise in natural text understanding. To close the gap, we introduce a neurosymbolic language called Logitext that allows the logical structure of text to be elaborated explicitly in formal notation. Logitext is represented internally by a novel form of natural language constraints. We show how to solve these constraints using an algorithm that combines ideas from textual gradient descent and Boolean Satisfiability (SAT) solving. The algorithm serves as a theory that extends a traditional Satisfiability Modulo Theory (SMT) solver, enabling fine-grained joint logical and NL-based reasoning. Our measurements show significant benefit from this joint reasoning toward addressing the reasoning gaps above.

TL;DR: A way to unify statistical and logical language understanding via a SMT theory of natural language text constraints.