This document explains how to fill out the Number page of the Grammar Matrix Customization questionnaire and presents background information on the number library of the Grammar Matrix Customization System (Bender et al., 2002; Bender and Flickinger, 2005; Bender et al., 2010). General instructions on using the questionnaire can be found here.

The standard reference for the Number Library and its implementations is Drellishak 2009. The full reference and .bib entry can be found here.

On the Number page in Matrix Customization you are asked to describe number marking in your language (e.g. singular, dual, plural). This can be defined as a hierarchy. The number library allows you to specify the range of values for the feature NUMBER that will be available elsewhere in the customization system and in the resulting grammar (see more on that in the Analyses section below). The complexity of number hierarchy is different for all languages. The number of values that you can enter for number names and their supertypes in questionnaire is unlimited.

Please note that this part of the questionnaire is for entering number values, and NOT numerals, such as one, two, three, etc.. Even though there can be an interaction between grammatical number and numerals, numerals are a very different phenomenon, which is not yet supported by the Matrix Customization system.

The values you define for number marking will be available to use later in the customization system, especially the Morphology and Lexicon pages. The answers you provide on this page will determine the values available on the Lexicon page for the NUM feature (or the PERNUM feature, about which see the Person section of the questionnaire for more details or Person documentation page). Note that feature values defined on the lexicon and morphology pages may affect the hierarchy of number. Underspecifications in the lexicon or morphosyntax will automatically be integrated in the hierarchy of number: you do not need to define these explicitly on the number page.

Using the dropdown menu, please add numbers and their supertypes as applicable to your language. Unlike gender, which focuses first and foremost on agreement, it is important to represent a number hierarchy for the grammar even if it is not involved in agreement. This is necessary to assure a consistent semantic representation of number, which needs to be reflected in your grammar. An example of a language with lack of number agreement between nouns and other parts of speech is Japanese. Despite this lack of agreement, both singular and plural numbers should be distinguished in the grammar. Otherwise the grammar cannot distinguish the semantics of sentences containing nouns that differ in number.

Some of the common possibilities of the number values on this page are: singular (represents one entity), dual (two entities), trial (three entities), quadral (four entities), paucal (a few entities), plural (multiple entities), general (unspecified number of entities), with some further subdivisions for paucal and plural numbers.

Below is an example of options chosen for Slovene, which has three numbers and a facultative number system (see Analyses for more details):

• Gender	Supertype
  Singular	number
  Dual	number
  Plural	number

For more information on how to use the questionnaire to define values for NUMBER in your language, please refer to the number page in Matrix Customization.

For more information on the implementation of number in Grammar Matrix please refer to the section Analyses.

Instead of applying some form of a universal number hierarchy to all starter grammars, the customization system requires users to define number values in their language, thus solving the problem with representing languages with complex number hierarchies, which cannot be accounted for by a universal number hierarchy. Examples of such number hierarchies that cannot be covered by a universal number hierarchy are found in languages with facultative number systems, in which number is present optionally.

American Sign Language is an example of a language with a number hierarchy that cannot be covered by a universal approach. While American Sign Language requires a hierarchy with plural and non-plural numbers (with the latter subdivided into singular and dual numbers), an attempt of a universal number hierarchy is likely to start with a singular vs. non-singular division (where non-singular may be further subdivided in dual and plural numbers, for instance). Because of the existence of languages that require different basic subdivisions, a customized Grammar Matrix approach is a better solution for representing number hierarchies across languages. For more information on merging person and number for your target language, please refer to Drellishak 2009, Section 5.3.6.1.

If you define a number hierarchy, your starter grammar will include the feature [ NUM number ], with possible values based on the choices you make on the number customization page. Note that like GENDER and PERSON, NUM is a feature of the nominal INDEX. Making NUM a feature of the semantic INDEX instead of the syntactic HEAD results in semantic representations of number in your grammar and avoids spurious ambiguity during generation.

Below is an example of a gender section in the choices file of a language with singular, plural, and dual numbers:

section=number
  number1_name=singular
    number1_supertype1_name=number
  number2_name=dual
    number2_supertype1_name=number
  number3_name=plural
    number3_supertype1_name=number

This will be reflected in the your_language_name.tdl file (given no additional information comes from the lexicon and morphology libraries):

png :+ [ PER person,
    NUM number,
    GEND gender,
    ANIMATION animation ].


;;; Number

number := *top*.
singular := number.
dual := number.
plural := number.

The choices you make on the number customization page, will also affect the lexical types (your_language_name.tdl file), lexical rules (lrules.tdl file), and inflectional rules (irules.tdl file).

The analyses implemented in the number library are described in detail in Drellishak 2009, Section 5.3.

NUM is a feature often involved in agreement phenomena. These are handled through the lexicon and morphology libraries. The analyses of agreement implemented in the Grammar Matrix are described in detail in Drellishak 2009, Section 5.2.

Note that feature values defined on the lexicon and morphology libraries may affect the hierarchy for number. Underspecifications in the lexicon or morphosyntax will automatically be integrated in the hierarchy of number: you do not need to define these explicitly on the number page. In the example above, for instance, if a lexical item or morpheme were to be defined that can be dual or plural (having both values assigned to the same entry on the morphology or lexical page), the hierarchy will look like this:

;;; Number

number := *top*.
singular := number.
non-singular := number.
dual := non-singular.
plural := non-singular.

• [ This documentation is under construction. When it is more complete, this section should describe any modifications to or enhancements of this library that are either in progress or planned. ]

Drellishak, S. (2009). Widespread but Not Universal: Improving the Typological Coverage of the Grammar Matrix. PhD thesis, University of Washington.

bibtex:

@phdthesis{Drellishak:09,
author = {Scott Drellishak},
year = {2009},
title = {Widespread but Not Universal: Improving the Typological Coverage of the {G}rammar {M}atrix},
school = {University of Washington}
}