Structural Disambiguation With Constraint Propagation

STRUCTURAL DISAMBIGUATION WITH CONSTRAINT PROPAGATION Hiroshi Maruyama IBM Research, Tokyo Research Laboratory 5-19 Sanbancho, Chiyoda-ku, Tokyo 102 Japan maruyama@jpntscvm.bitnet Abstract We present a new grammatical formalism called Con- straint Dependency Grammar (CDG) in which every grammatical rule is given as a constraint on word- to-word modifications. CDG parsing is formalized as a constraint satisfaction problem over a finite do- main so that efficient constraint-propagation algo- rithms can be employed to reduce structural am- biguity without generating individual parse trees. The weak generative capacity and the computational complexity of CDG parsing are also discussed. 1 INTRODUCTION We are interested in an efficient treatment of struc- tural ambiguity in natural language analysis. It is known that "every-way" ambiguous constructs, such as prepositional attachment in English, have a Cata- lan number of ambiguous parses (Church and Patil 1982), which grows at a faster than exponential rate (Knuth 1975). A parser should be provided with a disambiguation mechanism that does not involve generating such a combinatorial number of parse trees explicitly. We have developed a parsing method in which an intermediate parsing result is represented as a data structure called a constraint network. Every solution that satisfies all the constraints simultaneously corre- sponds to an individual parse tree. No explicit parse trees are generated until ultimately necessary. Pars- ing and successive disambiguation are performed by adding new constraints to the constraint network. Newly added constraints are efficiently propagated over the network by Constraint Propagation (Waltz 1975, Montanari 1976) to remove inconsistent values. In this paper, we present the basic ideas of a formal grammatical theory called Constraint Depen- dency Grammar (CDG for short) that makes this parsing technique possible. CDG has a reasonable time bound in its parsing, while its weak generative capacity is strictly greater than that of Context Free Grammar (CFG). We give the definition of CDG in the next section. Then, in Section 3, we describe the parsing method based on constraint propagation, using a step-by- step example. Formal properties of CDG are dis- cussed in Section 4. 31 2 CDG: DEFINITION Let a sentence s = wlw2 ... w,, be a finite string on a finite alphabet E. Let R -- {rl,r2,...,rk} be a finite set of role-iris. Suppose that each word i in a sentence s has k-different roles rl(i), r2(i) .... , rk(i). Roles are like variables, and each role can have a pair <a, d> as its value, where the label a is a member of a finite set L = {al,a2,...,at} and the modifiee d is either 1 < d < n or a special symbol nil. An analysis of the sentence s is obtained by assigning appropriate values to the n x k roles (we can regard this situation as one in which each word has a frame with k slots, as shown in Figure 1). An assignment A of a sentence s is a function that assigns values to the roles. Given an assignment A, the label and the modifiee of a role x …

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