Parsing with restricted quantification: an initial demonstration1

Abstract

The primary goal of this paper is to illustrate how smaller deductive search spaces can be obtained by extending a logical language with restricted quantification and tailoring an inference system to this extension. The illustration examines the search spaces for a bottom-up parse of a sentence with a series of four strongly equivalent grammars. The grammars are stated in logical languages of increasing expressiveness, each restatement resulting in a more concise grammar and a smaller search space.A secondary goal is to point out an area where further research could yield results useful to the design of efficient parsers, particularly for grammatical formalisms that rely heavily on feature systems.L'objectif principal de cet article est de montrer comment on peut obtenir de plus petits espaces de recherche deductive en ttendant un langage logique avec une quantification restreinte et en adaptant un systkme d'inference a cette extension. On examine les espaces de recherche Crees par un analyse ascendante d'une phrase faite a I'aide de quatre grammaires fortement tquivalentes. Chacune des grammaires est dtfinie avec un langage logique plus expressif que celui de la grammaire prkddente. Chaque redefinition permet d'obtenir une grammaire plus concise et un espace de recherche plus restreint.Un des objectifs secondaires de cet article est de pointer les endroits oB des recherches permettraient d'obtenir des resultats utiles pour la conception d'analyseurs efficaces, plus particulierement pour des formalismes grammaticaux qui reposent principalement sur des systhes de traits.Mots clh: analyse, quantification restreinte, logique avec esptxes, grammaires logiques, deduction automatique, traitement automatique du langage naturel, linguistique informatique, raisonnement automatist, strategic de recherche B implication minimale, systemes de traits, unification avec esj&ces, report de contraintes.

ProGram — a development tool for GPSG grammars

“…In either case it is difficult to avoid wasting time by following paths that cannot succeed due to earlier but as yet unchecked violations. An alternative which overcomes this problem is to carry out the checking incrementally, an approach which would require sophisticated inference mechanisms of the sort described in Frisch (1985), but which are not readily available in current programming languages. A bottom-up parser, on the other hand, starts off with fully instantiated lexical categories, and with care can insure that categories are always fully specified and checked before they are used elsewhere.…”

Taxonomic reasoning with many-sorted logics

“…Walther (1987) also presents the results of running other problems in both sorted and unsorted formalizations which all demonstrate the computational advantages that may be gained by encoding a problem in many sorted logic. De Champeaux (1978), Ohlbach & Schmidt-Schauss (1985) and Frisch (1985Frisch ( , 1986 also present examples of the computational power of many-sorted logic achieved by reductions in the search space compared to an unsorted formulation. We shall assume the reader has a basic knowledge of the first-order predicate calculus and of Resolution (see Bundy, 1983b;Wos et al, 1984or Genesereth & Nilsson, 1987 for example).…”