Two linguistic levels of lexical ambiguity and a unified categorical representation

Lexical disambiguation is one of the oldest problems in natural language processing. There are three main types of lexical ambiguity: part-of-speech ambiguity, homonymy, and polysemy, typically divided into two tasks in practice. While this division suffices for engineering purposes, it does not align well with human intuition. In this article, I use lexical ambiguity as a representative case to demonstrate how insights from theoretical linguistics can be helpful for developing more human-like meaning and knowledge representations in natural language understanding. I revisit the three types of lexical ambiguity and propose a structured reclassification of them into two levels using the theoretical linguistic tool of root syntax. Recognizing the uneven expressive power of root syntax across these levels, I further translate the theoretical linguistic insights into the language of category theory, mainly using the tool of topos. The resulting unified categorical representation of lexical ambiguity preserves rootsyntactic insights, has strong expressive power at both linguistic levels, and can potentially serve as a bridge between theoretical linguistics and natural language understanding.