Statistical Parsing for Logical Information Retrieval

TL;DR

This paper advances logical information retrieval by integrating a probabilistic graphical model with natural language parsing, enabling robust reasoning and semantic interpretation with high accuracy, bridging formal semantics and neural models.

Contribution

It introduces an extended QBBN with negation, a typed logical language with modal quantifiers, and a deterministic syntax parser, combining formal semantics with LLM-based disambiguation.

Findings

Engine handles 44 reasoning patterns successfully.

Grammar achieves 33/33 correct parses with zero ambiguity.

LLMs achieve 95% PP attachment accuracy but limited structured parse accuracy.

Abstract

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