Schema and salience in cognitive linguistics: a computational model of the ambiguity-vagueness spectrum
Geeraerts (1993) and Tuggy (1993) have argued that traditional tests for ambiguity can produce contradictory indications. For example, Geeraerts found that the linguistic test, based on anaphora, did not identify the English noun dog as ambiguous (basic dog versus male dog), but that the logical criterion, based on the acceptability of sentences like "this dog is not a dog", did. (See, however, Dunbar, 2001, for a different analysis and interpretation of this.) Tuggy (1993) agrees with Geeraerts' general position, concluding that there is no fixed boundary between cases of ambiguity and vagueness, with a continuum of polysemy ranging between these poles.
Tuggy analyses this continuum using Cognitive Grammar (Langacker, 1992). Related meanings are linked by a schema. At one extreme the schema is 'well-entrenched', and the meanings are not themselves well-entrenched. This represents a vague category. At the opposite pole the separate readings are well-entrenched and there is no subsuming schema. This is ambiguity. In between, there can be variation in the salience of the schema or the elaborative distance between schema and instances. In Tuggy's model there is a parameter that adjusts a threshold for salience, so that items become effectively ambiguous if there is no subsuming schema whose salience is greater than the current threshold.
This paper presents a computational model that implements Tuggy's account using Adaptive Resonance Theory, a type of connectionist model (Carpenter & Grossberg, 1987; Dunbar, 1999). The model stores concepts as prototypes. When a new instance is encountered, the model compares it to the stored concepts, and selects the most similar one. It then retrieves the prototype for that concept and compares it to the instance. There are two possible outcomes at this stage. If the instance is sufficiently similar, it is assimilated to the existing concept, whose prototype is modified slightly to allow for variation in the new instance. This corresponds to the case of vagueness. The other possible outcome is that the instance is not sufficiently similar. Then the model will set up a new concept, initially with the novel instance as its prototype. This corresponds to ambiguity, with a distinct concept being 'entrenched' separately. The computational model contains a parameter termed 'vigilance', and it is shown that manipulating this generates the ambiguity-vagueness spectrum described by Geeraerts and Tuggy.
Carpenter, G. A. and Grossberg, S. (1987). ART 2: Self-organization of stable category recognition codes for analog input patterns. Applied Optics 26, 4919-4930.
Dunbar, G. L. (1999). The clustering of natural terms: an Adaptive Resonance Theory model. Proceedings of the International Joint Conference on Neural Networks, Washington D.C.
Dunbar, G. L. (2001). Towards a cognitive analysis of polysemy, ambiguity, and vagueness. Cognitive Linguistics, 12, 1-14.
Geeraerts, D. (1993). Vagueness's puzzles, polysemy's vagaries. Cognitive Linguistics, 4, 223-272.
Langacker, R. W. (1992). Foundations of Cognitive Grammar. Vol. 1: Theoretical Prerequisites. Stanford, CA: Stanford University Press.
Tuggy, D. (1993). Ambiguity, polysemy and vagueness. Cognitive Linguistics, 4, 273-290.