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

arXiv: https://arxiv.org/abs/2510.06559 · HTML: https://mlsanity.com/paper/2510.06559/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 20 references that are in the map.
- First posted on arXiv 8 Oct 2025.

## Builds on (most cited first, 9 of 9)

- [Navigating LLM Ethics: Advancements, Challenges, and Future Directions](https://mlsanity.com/paper/2406.18841/) (2024)
- [Building Ethically Bounded AI](https://mlsanity.com/paper/1812.03980/) (2018)
- [Mapping the Neuro-Symbolic AI Landscape by Architectures: A Handbook on Augmenting Deep Learning Through Symbolic Reasoning](https://mlsanity.com/paper/2410.22077/) (2024)
- [Unpacking the Ethical Value Alignment in Big Models](https://mlsanity.com/paper/2310.17551/) (2023)
- [Towards a Benchmark for Causal Business Process Reasoning with LLMs](https://mlsanity.com/paper/2406.05506/) (2024)
- [A Statistical Case Against Empirical Human-AI Alignment](https://mlsanity.com/paper/2502.14581/) (2025)
- [A Reality check of the benefits of LLM in business](https://mlsanity.com/paper/2406.10249/) (2024)
- [A type theoretical framework for natural language semantics: the Montagovian generative lexicon](https://mlsanity.com/paper/1301.4938/) (2013)
- [KRAFT -- A Knowledge-Graph-Based Resource Allocation Framework](https://mlsanity.com/paper/2503.21636/) (2025)

## Abstract (arXiv)

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.