Abstract: | Longstanding theoretical debates about whether structure A or structure B is the correct analysis of phenomenon X are commonplace. For example, at the juncture of two words W1 and W2, French liaison consonants alternate with zero. Theories of French phonology have long debated whether the consonant is associated with W1 or W2. In this work, we argue for an alternative approach. Phenomena X is not accounted for by either A or B, but rather a conjunctive blend of structures A and B. This notion of 'blend of structures' is formalized using Gradient Symbolic Representations, symbol structures in which a particular position is generally occupied by a sum of gradient symbols, each symbol having a partial degree of presence: its activity. The grammatical consequences of a Gradient Symbolic Representation are the sum of the consequences of all the symbols blended to form it; the consequences of a symbol - e.g., the costs of constraint violations - are proportional to its activity. The proposed grammatical computation consists of optimization with respect to a numerical weighting of familiar phonological constraints from Optimality Theory and Harmonic Grammar, straightforwardly extended to evaluate Gradient Symbolic Representations. We apply this general framework to French liaison consonants, blending together elements of previous proposals to give a single analysis that covers a wide range of data not previously explicable within a single theory. |