Adam Kilgarriff (1992) devotes his thesis to a discussion of polysemy. The essential conclusion which he draws, on the basis of considerations of the traditional distinction drawn between homonymy and polysemy and of investigation of lexicographic techniques for delimiting dictionary senses, is that ``Polysemy does not form any kind of `natural kind''' (Kilgarriff 1992:4). Instead, polysemy describes a ``crossroads'' between homonymy, alternations, collocations and analogy based on general knowledge and reasoning. Polysemous words can be characterised by at least one of these four methodologies, and Kilgarriff argues that all four must be allowed for in order to capture the full variety of polysemy.
Kilgarriff observes, however, that collocations and analogy depend on frequency information and are subject to contextual variation while description of homonymy and alternations relies on rules, and that joining the two approaches involves augmenting formal lexical structure with frequency data. This view is supported by the results of my investigation of logical metonymy (Chapter 5), which suggests that conventionality plays an important role in predicting language use. The computational lexicon must therefore both reflect linguistic generalisations and provide information on conventional language usage.
The main implication of this work is that polysemy is not a term which can be applied to characterise word senses in an entirely precise way. There cannot be clear-cut tests for identifying polysemy due to its multi-faceted nature. Homonymy is not orthogonal to polysemy, but rather an endpoint of one of the dimensions along which polysemy can be described (fully predictable sense variation -- unpredictable sense variation). Furthermore, most words display some variation in the meaning they express and the criteria for pinning down senses are often dependent on questions of frequency and predictability rather than on clearly delineated distinctions. For the purposes of designing a lexicon for an NLU/NLG system, that means distinguishing senses of a word when there are syntactic differences in the way that word is used, and when there are variations in meaning which seem to follow from general, productive relationships.