The Algebra of Meaning: Why Machines Need Montague More Than Moore's Law

• URL: http://arxiv.org/abs/2510.06559v1
• Date: Wed, 08 Oct 2025 01:22:26 GMT
• Title: The Algebra of Meaning: Why Machines Need Montague More Than Moore's Law
• Authors: Cheonkam Jeong, Sungdo Kim, Jewoo Park,
• Abstract summary: We argue that moderation, brittle, and opaque semantics are symptoms of missing type-theoretic semantics rather than data or scale limitations.<n>Building on Montague's view of language as typed, compositional algebra, we recast alignment as a parsing problem.<n>We present Savai, a neuro-symbol-language that compiles utterances into descriptive-style logical forms.
• Score: 0.32904041852873017
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Contemporary language models are fluent yet routinely mis-handle the types of meaning their outputs entail. We argue that hallucination, brittle moderation, and opaque compliance outcomes are symptoms of missing type-theoretic semantics rather than data or scale limitations. Building on Montague's view of language as typed, compositional algebra, we recast alignment as a parsing problem: natural-language inputs must be compiled into structures that make explicit their descriptive, normative, and legal dimensions under context. We present Savassan, a neuro-symbolic architecture that compiles utterances into Montague-style logical forms and maps them to typed ontologies extended with deontic operators and jurisdictional contexts. Neural components extract candidate structures from unstructured inputs; symbolic components perform type checking, constraint reasoning, and cross-jurisdiction mapping to produce compliance-aware guidance rather than binary censorship. In cross-border scenarios, the system "parses once" (e.g., defect claim(product x, company y)) and projects the result into multiple legal ontologies (e.g., defamation risk in KR/JP, protected opinion in US, GDPR checks in EU), composing outcomes into a single, explainable decision. This paper contributes: (i) a diagnosis of hallucination as a type error; (ii) a formal Montague-ontology bridge for business/legal reasoning; and (iii) a production-oriented design that embeds typed interfaces across the pipeline. We outline an evaluation plan using legal reasoning benchmarks and synthetic multi-jurisdiction suites. Our position is that trustworthy autonomy requires compositional typing of meaning, enabling systems to reason about what is described, what is prescribed, and what incurs liability within a unified algebra of meaning.

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