Towards Uniform Processing of Constraint-based Categorial Grammars

A class of constraint-based categorial grammars is proposed in which the construction of both logical forms and strings is specified completely lexically. Such grammars allow the construction of a uniform algorithm for both parsing and generation. Termination of the algorithm can be guaranteed if lexical entries adhere to a constraint, that can be seen as a computationally motivated version of GB's projection principle. 1 M o t i v a t i o n s In constraint-based approaches to grammar the semantic interpretation of phrases is often defined in the lexical entries. These lexical entries specify their semantic interpretation, taking into account the semantics of the arguments they subcategorize for (specified in their subcat list). The grammar rules simply percolate the semantics upwards; by the selection of the arguments, this semantic formula then gets further instantiated (Moore, 1989). Hence in such approaches it can be said that all semantic formulas are 'projected from the lexicon' (Zeevat et al., 1987). Such an organization of a grammar is the starting point of a class of generation algorithms that have become popular recently (Calder et al., 1989; Shieber et al., 1989; Shieber el al., 1990). These semantic-head-driven algorithms are both geared towards the input semantic representation and the information contained in lexical entries. If the above sketched approach to semantic interpretation is followed systematically, it is possible to show that such a semantic-head-driven generation algorithm terminates (Dymetman et al., 1990). In van Noord (1991) I define a head-driven parser (based on Kay (1989)) for a class of constraint-based grammars in which the construction of strings may use more complex operations that simple context-free concatenation. Again, this algorithm is geared towards the input (string) and the information found in lexical entries. In this paper I investigate an approach where the construction of strings is defined lexically. Grammar rules simply percolate strings upwards. Such an approach seems feasible if we allow for powerful constraints to be defined. The head-corner parser knows about strings and performs operations on them; in the types of grammars defined here these operations are replaced by general constraint-solving techniques (HShfeld and Smolka, 1988; Tuda et al., 1989; Damas et al., 1991). Therefore, it becomes possible to view both the head-driven generator and the head-driven parser as one and the same algorithm. For this uniform algorithm to terminate, we generalize the constraint proposed by Dymetman et ai. (1990) to both semantic interpretations and strings. That is, for each lexical entry we require that its string and its semantics is larger than the string and the semantics associated with each of its arguments. The following picture then emerges. The depth of a derivation tree is determined by the subcat list of the ultimate head of the tree. Furthermore, the string and the semantic representation of each of the non heads in the derivation tree is determined by the subcat list as well. A specific condition on the relation between elements in the subcat list and their se-