Grammar-Writing/Universal-Types

The Notation for Declaring Types and Subtypes in this Wiki

type1
   type2 (= first immediate subtype of type1)
      type21 (= first immediate subtype of type2)
      type22 (= second immediate subtype of type2)
      type23 (= third immediate subtype of type2)
   type3 (= second immediate subtype of type1)
 

The Notation for Declaring Features in this Wiki

To declare that type23 has the features feature1, feature2, ..., feature5 with values type1, type2, ..., type5, we write:

type23 feature1:type1 feature2:type2 ... feature5:type5

Types That Appear in Every Grammar

bool(ean)

This type is named after the English logician George Boole, who developed what is now called Boolean algebra. According to Wikipedia, this is the branch of algebra in which the values of the variables are the truth values true and false ...

In linguistics, it is customary to use plus and minus instead of true and false.

Formal Definition

bot
   bool
      plus
      minus
 

Informally: bool is an immediate subtype of bot and has the two immediate subtypes plus and minus. None of the three types bool, plus, and minus introduces any features.

Example

The type is used as the value of the feature AUX to distinguish between main and auxiliary verbs:

auxiliaries: [AUX plus]
main verbs: [AUX minus] .

list

A list is an ordered collection of elements. There are two types of lists:

1. The empty list (e_list): it has no elements in it.
2. The non-empty list (ne_list): it consists of two parts, a head (hd)element (which can be an any type) and a tail (tl) (the rest of the list, which is also a list).

Formal Definition

bot
   list
      e_list
      ne_list hd:bot tl:list
 

Informally: list is an immediate subtype of bot and has the two immediate subtypes e_list and ne_list. The types list and e_list introduce no features. The type ne_list introduces the features hd with value bot and tl with value list.

Notational simplifications

a. < > is short for e_list.

b. <A> is short for (hd:A,
                     tl:e_list).

c. <A,B> is short for (hd:A,
                       tl:(hd:B,
                           tl:e_list)) .

Example

The type is used as the value of the valence features SUBJ, SPR, and COMPS.

• a SUBJ list that is empty: [SUBJ < >] .

• a COMPS list that contains an NP and a PP: [COMPS <NP,PP>].