Feature Matrices and Agreement

by Remi van Trijp, Sony Computer Science Laboratory Paris

This demonstration provides examples of how feature matrices optimize processing in Fluid Construction Grammar. You can click on all boxes to inspect several parts of the demo, including linguistic constructions and search trees in processing. The demonstration supports the following paper:

• van Trijp, Remi (2011). Feature Matrices and Agreement: A Case Study for German Case. In: Steels, Luc (ed.), Design Patterns in Fluid Construction Grammar, pp. 205--235, Amsterdam: John Benjamins.

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The Importance of Processing-Friendly Representations

Many feature-structure grammar formalisms use disjunctive feature representation for multifunctional forms. Disjunctions simply list the possibilities, for instance the German definite article die can be mapped onto the following values for case, number and gender: {NOM.SG.F, NOM.PL, ACC.SG.F, ACC.PL}. Disjunctions look as if they are very elegant because of their short notation style, but they are in fact very expensive in processing. This can be illustrated through the following example sentence:

die	Kinder	gaben	der	Lehrerin	die	Zeichnung
the.NOM.PL	children	gave	the.DAT.SG.F	(female) teacher	the.ACC.SG.F	drawing
'The children gave the drawing to the (female) teacher.'

Even though this utterance is unambiguous to native speakers of German, we soon see an explosion of the search space when parsing the utterance if we use disjunctions to represent the multiple functions of the definite articles:

Parsing "die Kinder gaben der Lehrerin die Zeichnung" (all solutions)

Computing all solutions for application of

construction set (8)

in direction ←

Parsed meanings

meaning 1

Feature Matrices

Processing German case forms is regarded as one of the hardest problems for unification-based grammars, and several researchers have proposed type hierarchies for solving the efficiency issues of disjunctions. However, most of these solutions still need to be combined with disjunctions, which leads to implausible models of processing. The paper proposes feature matrices as an alternative solution. Here, we see that feature matrices drastically reduce the search space:

Parsing "die Kinder gaben der Lehrerin die Zeichnung" (all solutions)

Computing all solutions for application of

construction set (12)

in direction ←

Parsed meanings

meaning 1