Montagovian Definite Clause Grammar

This paper reports a completed stage of ongoing research at the University oF York. Landsbergen's advocacy of analytical inverses ~or compositional suntax rules encourages the application of Definite Clause Grammar techniques to the cons-t~uction of a parser returning Montague analysis trees. A parser MDCg is presented which implements an augmented Friedman-Warren algorithm permitting post referencing, and interfaces with a language oF intensional logic translator LILT so as to display the dorivattonal history of corresponding reduced IL Form-ulae. Some familiarity with Montague's PTG and the basic DCQ mechanism is assumed. Consideration is given by Landsbergen (20] to the global algorithmic structure of a top down parser demonstrably equivalent to a compositional grammar such as that of PTG [223. The method is as Follo~s: 1. Formulate the original grammar in te~ms of indexed compositional-M rules of form: If syntax trees ~Sk..Sn) satisf~ condition C then combine <Sk.. Sn~ into Sj such that the compositional history may be represented on a derivation tree (i.e. a skeletal analgsis tree lacking node labels). ~. Subject to specified restraints evolve inverse analytical-M Rules of form: If Sj conforms to condition C" then analgse Sj into <Sk..Sn~. 3. P~ove that the composltional and analytical M ~ules are equivalent. 4. Construct a two stage parser: (i) Parse • sentence using a context free grammar (CFg) thus deriving a syntax tree. (ii) Traverse the svntax tree in postorder [19] under the guidance of the analytical-M rules, constructing the derivation tree which reflects the reverse order application of the inverse rules. An abstract algorithm describing the parser is given in the Form of procedural pseudo code, however the problem of establlshing that an implementation conForms to the algorithm is deferred, a problem perh • ps aggravated bv the absence Of • Formal notation for M rules which might otherwise have suggested appropriate data structures. The postorder traverse in (ii) of a preorder ere • tiDe involves a duplication which may be • voided by • dopting the PROLOG Definite Clause grammar (DCg) formalism, (C28] of. [3], £4], C5], [21]), which, as has been observed [32] virtually forces the methodology of syntax directed translation coupled with compositional semantics. A DCG may be ingenuously characterised as a CFQ having category sumbols augmented by argument places, and cont • ining supplementary goals not limited in function to input consumption.. Logical variables in argument places permit synthesised and inherited attributes (18] to be handled …