用概率图模型实现自然语言逻辑推理，支持正反向推导与语法结构解析。
Statistical Parsing for Logical Information Retrieval
- 引入负因子和反向消息传递，实现逆否推理（模态否定）
- 44组测试用例全通过，33个句子语法解析正确无歧义
- 结合LLM与形式化语法，适合需要严谨逻辑的AI系统
此前工作（Coppola, 2024）提出了量化布尔贝叶斯网络（QBBN），一种将自然演绎前向片段（Prawitz, 1965）建模为概率因子图的逻辑图形模型。本文填补两大空白：缺乏否定/反向推理，以及无自然语言解析器。在推理方面，扩展QBBN加入负因子（满足P(x) + P(¬x) = 1），通过反向λ消息实现逆否推理（模态否定），完整覆盖Prawitz的简化消去规则，引擎在44/44测试用例中成功处理22种推理模式。语义层面，提出带类型的角色标注谓词语言，包含模态量词与三层表达力：一阶量词、命题作为参数、通过λ抽象实现谓词量词。句法方面，设计类型化槽语法，可确定性地将句子编译为逻辑形式（33/33正确，零歧义）。虽然大模型在消歧上表现良好（95%依从准确率），但无法直接生成结构化解析（仅12.4%平均弧精度），证实语法必要性。整体架构为：大模型预处理 → 语法解析 → 大模型重排序 → QBBN推理。我们认为该框架调和了形式语义与Sutton的‘苦涩教训’（2019）：大模型消除标注瓶颈，充当注释者，而QBBN则充当验证者。
原文摘要 · Abstract (English)
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
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