A vector logic for intensional formal semantics

• URL: http://arxiv.org/abs/2602.02940v1
• Date: Tue, 03 Feb 2026 00:24:37 GMT
• Title: A vector logic for intensional formal semantics
• Authors: Daniel Quigley,
• Abstract summary: Formal semantics and distributional semantics are distinct approaches to linguistic meaning.<n>This paper proves that these frameworks are structurally compatible for intensional semantics.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Formal semantics and distributional semantics are distinct approaches to linguistic meaning: the former models meaning as reference via model-theoretic structures; the latter represents meaning as vectors in high-dimensional spaces shaped by usage. This paper proves that these frameworks are structurally compatible for intensional semantics. We establish that Kripke-style intensional models embed injectively into vector spaces, with semantic functions lifting to (multi)linear maps that preserve composition. The construction accommodates multiple index sorts (worlds, times, locations) via a compound index space, representing intensions as linear operators. Modal operators are derived algebraically: accessibility relations become linear operators, and modal conditions reduce to threshold checks on accumulated values. For uncountable index domains, we develop a measure-theoretic generalization in which necessity becomes truth almost everywhere and possibility becomes truth on a set of positive measure, a non-classical logic natural for continuous parameters.

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