Semantic Field Theory

A Cohomological Field Theory of Meaning over Structured Spaces
AAD Systems™ · 2026
Abstract. We introduce a cohomological field theory in which meaning is modeled as a section-valued field over structured spaces. Local semantic regimes correspond to sections, while global meaning arises through descent along admissible transformations. Failures of semantic consistency are classified as cohomological obstructions, establishing a correspondence between semantics, geometry, and physical theory.

1. Structured Semantic Spaces

Let X be a structured space. A semantic system assigns local meaning:

F : X → 𝒞

where 𝒞 is a category of semantic objects.

2. Semantic Fields

A semantic field is a section:

s ∈ Γ(X, F)

Local sections define semantic regimes.

3. Descent and Global Meaning

sᵢ |Uᵢ ∩ Uⱼ = sⱼ |Uᵢ ∩ Uⱼ

Meaning exists when local sections glue consistently.

4. Cohomological Obstructions

[ω] ∈ H¹(X, F)

Nontrivial classes represent semantic inconsistency.

5. Correspondence Principle

Semantics ↔ Geometry ↔ Physical Theory

Meaning is invariance under admissible transformations.

This document defines the foundational framework underlying subsequent research in semantic systems, cohomology, and invariant computational structures.