Reflexive binding and reconstruction in a Multi-modal TLG
This paper deals with reflexive finding in Wh-extraction constructions. Binding of a reflexive in a fronted Wh-phrase poses two technical problems for Lambek Calculus. First, the standard locality constraint on reflexive binding seems violated in the surface syntax. To deal with this, a Chomskian syntactic theory may apply the locality constraint with regard to the position of the trace or the tail copy of the fronted Wh-expression. However, Lambek Calculus merges the category for the Wh-expression only in its phonological position and thus, achieving the desirable effect of the reconstruction as used in Chomskian syntactic theories requires an extra innovation. Secondly, reflexive binding is problematic for the resource sensitivity of Lambek Calculus, since in the semantic representation for the sentence, the semantic term for the antecedent NP is duplicated while the contribution of the reflexive is not clear. I deal with both the problems by way of modally controlled structural rules in a Multi-modal extension of non-commutative, non-associative Lambek Calculus NL. For the lexical assignment to the reflexive, I use a modified type logical implementation of Pauline Jacobson’s pronominal functor category. This reflexive functor requires insertion of a hypothetical argument as its right sister in the categorial proof. The hypothetical category is then moved via modally controlled structural rules to a position that satisfies the above-mentioned locality constraint. Every hypothetical category disappears by the end of the categorial proof and thus does not correspond to an item in the phonological string. Because of this, ‘moving’ the position of the hypothetical category for the reflexive during a cateogrial proof does not affect the position of the reflexive in the phonological string. For the duplication of the antecedent resource, I postulate a modally controlled contraction rule in the categorial calculus. The resultant sequent calculus does not maintain the subformula property in its strict sense. This could make the calculus undecidable. However, since each application of the contraction rule requires a distinguished occurrence of the reflexive functor category in the antecedent structure, we can maintain a weakened version of sub-formula property.