Structural Equations in Language Learning

In categorial systems with a fixed structural component, the learning problem comes down to finding the solution for a set of typeassignment equations. A hard-wired structural component is problematic if one want to address issues of structural variation. Our starting point is a type-logical architecture with separate modules for the logical and the structural components of the computational system. The logical component expresses invariants of grammatical composition; the structural component captures variation in the realization of the correspondence between form and meaning. Learning in this setting involves finding the solution to both the type-assignment equations and the structural equations of the language at hand. We develop a view on these two subtasks which pictures learning as a process moving through a two-stage cycle. In the first phase of the cycle, type assignments are computed statically from structures. In the second phase, the lexicon is enhanced with facilities for structural reasoning. These make it possible to dynamically relate structures during on-line computation, or to establish off-line lexical generalizations. We report on the initial experiments in [15] to apply this method in the context of the Spoken Dutch Corpus. For the general type-logical background, we refer to [12]; §1 has a brief recap of some key features. 1 Constants and variation One can think of type-logical grammar as a functional programming language with some special purpose features to customize it for natural language processing tasks. Basic constructs are demonstrations of the form Γ ` A, stating that a structure Γ is a well-formed expression of type A. These statements are the outcome of a process of computation. Our programming language has a built-in vocabulary of logical constants to construct the type formulas over some set of atomic formulas in terms of the indexed unary and binary operations of (1a). Parallel to the formula language, we have the structure-building operations of (1b) with (· ◦i ·) and 〈·〉j as counterparts of •i and ♦j respectively. The indices i and j are taken from given, finite sets I, J which we refer to as composition modes. a. Typ ::= Atom | ♦jTyp | 2jTyp | Typ •i Typ | Typ/iTyp | Typ\iTyp b. Struc ::= Typ | 〈Struc〉j | Struc ◦i Struc (1)