Modeling Sentence Meaning Using Linear Operators in a Vector Space Semantics Framework: An Interdisciplinary Approach

This paper presents a simplified yet interdisciplinary framework for modeling sentence meaning by integrating foundational concepts from linguistic semantics and operator theory. The core idea is to represent content words, particularly nouns, as vectors in a high-dimensional semantic space, while function words such as adjectives and verbs are modeled as linear operators that act upon or combine these vectors. This approach allows for a structured and computationally tractable method of capturing compositional meaning in natural language. Using basic mathematical operations such as matrix multiplication and the tensor product, the paper demonstrates how meanings of phrases and sentences can be derived through illustrative examples like angry dog and dogs chase cats. These examples showcase how complex expressions are formed by systematically applying operators to simpler vector representations. By bridging the gap between formal linguistic theory and linear algebra, the proposed model offers an intuitive and rigorous framework for understanding how meaning emerges from the combination of words in context. Furthermore, this operator-theoretic perspective opens new avenues for the development of interpretable, modular, and potentially more sustainable natural language processing systems. The framework not only contributes to theoretical investigations in semantics but also holds promise for real-world applications in artificial intelligence, particularly in building transparent and explainable models for language understanding.