Tensor Logic of Embedding Vectors in Neural Networks

Current Artificial Neural Networks based on Large Language Models (LLMs) primarily use statistical token prediction, often lacking rigorous structural semantic consistency and illocutionary force. This paper introduces the textbf{Tensor Functional Language Logic (T-FLL)} as a formal bridge between symbolic reasoning and continuous neural manifolds. We redefine linguistic units as functional noemes and propose a mapping of logical operators onto tensor operations. Sentences are translated into emph{noematic formulae}, and we show that the attention mechanism driving the semantics of a dialog can be reformulated more efficiently if directed by the noematic formulae. In this way, we outline a path toward more explainable and structurally sound AI architectures.