Statistical Parsing for Logical Information Retrieval
This work addresses the problem of integrating logical reasoning with natural language processing for researchers in formal semantics and AI, offering a hybrid architecture that leverages LLMs to overcome annotation bottlenecks.
The paper tackles the gaps of lacking negation/backward reasoning and a natural language parser in the Quantified Boolean Bayesian Network (QBBN) by extending it with NEG factors for contrapositive reasoning and introducing a typed slot grammar for deterministic parsing, achieving 44/44 test cases in inference and 33/33 correct parses.
In previous work (Coppola, 2024) we introduced the Quantified Boolean Bayesian Network (QBBN), a logical graphical model that implements the forward fragment of natural deduction (Prawitz, 1965) as a probabilistic factor graph. That work left two gaps: no negation/backward reasoning, and no parser for natural language. This paper addresses both gaps across inference, semantics, and syntax. For inference, we extend the QBBN with NEG factors enforcing P(x) + P(neg x) = 1, enabling contrapositive reasoning (modus tollens) via backward lambda messages, completing Prawitz's simple elimination rules. The engine handles 44/44 test cases spanning 22 reasoning patterns. For semantics, we present a typed logical language with role-labeled predicates, modal quantifiers, and three tiers of expressiveness following Prawitz: first-order quantification, propositions as arguments, and predicate quantification via lambda abstraction. For syntax, we present a typed slot grammar that deterministically compiles sentences to logical form (33/33 correct, zero ambiguity). LLMs handle disambiguation (95% PP attachment accuracy) but cannot produce structured parses directly (12.4% UAS), confirming grammars are necessary. The architecture: LLM preprocesses, grammar parses, LLM reranks, QBBN infers. We argue this reconciles formal semantics with Sutton's "bitter lesson" (2019): LLMs eliminate the annotation bottleneck that killed formal NLP, serving as annotator while the QBBN serves as verifier. Code: https://github.com/gregorycoppola/world