The present paper constitutes a cognitive approach to the notion of ambiguity and vagueness in terms of polysemy. The author explores polysemy and, in particular, gradable categories in the lexicon by means of a computational cognitive model, the Adaptive Resonance Theory (ART). In particular, by means of three experiments, the study tests ART using entities with multiple meanings (pad, line, bank etc.), selected from the Cobuild Corpus. It is showed that there is variation in speakers responses; even for the same speaker a word may be polysemous in one case and vague in another depending on whether the vigilance or else the conceptual knowledge is high, the higher the vigilance (conceptual knowledge), the less vague a polysemous word is.