documenting math

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<P ALIGN="center"><CENTER><H1> Adjectives and adjectival phrases</H1>
<FONT SIZE="4">
<I>Author: </I><BR>
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</FONT></CENTER>
<P></P>

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<P ALIGN="center"><CENTER><H1> Adverbs and adverbial phrases</H1>
<FONT SIZE="4">
<I>Author: </I><BR>
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<P></P>

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<P ALIGN="center"><CENTER><H1> The category system</H1>
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<P></P>

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<P ALIGN="center"><CENTER><H1> Coordination</H1>
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<I>Author: </I><BR>
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<P></P>

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</HEAD><BODY BGCOLOR="white" TEXT="black">
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<HR NOSHADE SIZE=1>
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Author:
Last update: Tue Jan 31 18:15:47 2006
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<P>
Produced by
gfdoc - a rudimentary GF document generator.
(c) Aarne Ranta (<A HREF="mailto:aarne@cs.chalmers.se">aarne@cs.chalmers.se</A>) 2002 under GNU GPL.
</P>
<P>
==
</P>
<PRE>
abstract Demonstrative = Cat ** {
</PRE>
<P></P>
<P>
Naming convention: <CODE>M</CODE> prepended to 'unimodal' names.
Exceptions: lexical units, those without unimodal counterparts.
</P>
<PRE>
cat
MS ; -- multimodal sentence or question
MQS ; -- multimodal wh question
MImp ; -- multimodal imperative
MVP ; -- multimodal verb phrase
MComp ; -- multimodal complement to copula (MAP, MNP, MAdv)
MAP ; -- multimodal adjectival phrase
MNP ; -- multimodal (demonstrative) noun phrase
MAdv ; -- multimodal (demonstrative) adverbial
Point ; -- pointing gesture
fun
</PRE>
<P></P>
<P>
A pointing gesture is constructed from a string.
</P>
<PRE>
MkPoint : String -&gt; Point ;
</PRE>
<P></P>
<P>
Construction of sentences, questions, and imperatives.
</P>
<PRE>
MPredVP : MNP -&gt; MVP -&gt; MS ; -- he flies here
MQPredVP : MNP -&gt; MVP -&gt; MQS ; -- does he fly here
MQuestVP : IP -&gt; MVP -&gt; MQS ; -- who flies here
MImpVP : MVP -&gt; MImp ; -- fly here!
</PRE>
<P></P>
<P>
Construction of verb phrases from verb + complements.
</P>
<PRE>
MUseV : V -&gt; MVP ; -- flies (here)
MComplV2 : V2 -&gt; MNP -&gt; MVP ; -- takes this (here)
MComplVV : VV -&gt; MVP -&gt; MVP ; -- wants to fly (here)
MUseComp : MComp -&gt; MVP ; -- is here ; is bigger than this
MCompAP : MAP -&gt; MComp ; -- bigger than this
MCompNP : MNP -&gt; MComp ; -- the price of this
MCompAdv : MAdv -&gt; MComp ; -- here
MPositA : A -&gt; MAP ; -- big
MComparA : A -&gt; MNP -&gt; MAP ; -- bigger than this
</PRE>
<P></P>
<P>
Adverbial modification of a verb phrase.
</P>
<PRE>
MAdvVP : MVP -&gt; MAdv -&gt; MVP ; -- fly here
</PRE>
<P></P>
<P>
Demonstrative pronouns as NPs and determiners.
</P>
<PRE>
this_MNP : Point -&gt; MNP ; -- this
that_MNP : Point -&gt; MNP ; -- that
thisDet_MNP : CN -&gt; Point -&gt; MNP ; -- this car
thatDet_MNP : CN -&gt; Point -&gt; MNP ; -- that car
</PRE>
<P></P>
<P>
Demonstrative adverbs.
</P>
<PRE>
here_MAdv : Point -&gt; MAdv ; -- here
here7from_MAdv : Point -&gt; MAdv ; -- from here
here7to_MAdv : Point -&gt; MAdv ; -- to here
</PRE>
<P></P>
<P>
Building an adverb as prepositional phrase.
</P>
<PRE>
MPrepNP : Prep -&gt; MNP -&gt; MAdv ; -- in this car
</PRE>
<P></P>
<P>
Using ordinary categories.
Mounting nondemonstrative expressions.
</P>
<PRE>
DemNP : NP -&gt; MNP ;
DemAdv : Adv -&gt; MAdv ;
</PRE>
<P></P>
<P>
Top-level phrases.
</P>
<PRE>
PhrMS : Pol -&gt; MS -&gt; Phr ;
PhrMS : Pol -&gt; MS -&gt; Phr ;
PhrMQS : Pol -&gt; MQS -&gt; Phr ;
PhrMImp : Pol -&gt; MImp -&gt; Phr ;
</PRE>
<P></P>
<P>
For testing and example-based grammar writing.
</P>
<PRE>
point1, point2 : Point ;
}
</PRE>
<P></P>
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<P ALIGN="center"><CENTER><H1> The Main Module of the Resource Grammar</H1>
<FONT SIZE="4">
<I>Author: </I><BR>
Last update: Thu Jan 26 15:05:56 2006
Last update: Tue Jan 31 18:15:44 2006
</FONT></CENTER>
<P></P>

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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
<HTML>
<HEAD>
<META NAME="generator" CONTENT="http://txt2tags.sf.net">
<TITLE> The Mathematics API to the Resource Grammar</TITLE>
</HEAD><BODY BGCOLOR="white" TEXT="black">
<P ALIGN="center"><CENTER><H1> The Mathematics API to the Resource Grammar</H1>
<FONT SIZE="4">
<I>Author: </I><BR>
Last update: Tue Jan 31 18:15:47 2006
</FONT></CENTER>
<P></P>
<HR NOSHADE SIZE=1>
<P></P>
<UL>
<LI><A HREF="#toc1">The Mathematics API to the Resource Grammar</A>
</UL>
<P></P>
<HR NOSHADE SIZE=1>
<P></P>
<P>
Produced by
gfdoc - a rudimentary GF document generator.
(c) Aarne Ranta (<A HREF="mailto:aarne@cs.chalmers.se">aarne@cs.chalmers.se</A>) 2002 under GNU GPL.
</P>
<A NAME="toc1"></A>
<H1>The Mathematics API to the Resource Grammar</H1>
<P>
This grammar is a collection of the different modules.
It differs from <CODE>Lang</CODE> in two main ways:
</P>
<UL>
<LI>the combinations in Noun, Verb, Adjective, Adverb, Sentence are not included
<LI>instead, Symbol and Predication are used
</UL>
<P>
In practice, the most important difference is that only present-tense sentences
are included, and that symbolic expressions are recognized as NPs.
</P>
<PRE>
abstract Mathematical =
Noun - [ComplN2], --- to avoid ambiguity
</PRE>
<P></P>
<P>
Verb,
Adjective,
Adverb,
</P>
<PRE>
Numeral,
</PRE>
<P></P>
<P>
Sentence,
</P>
<PRE>
Question,
Relative,
Conjunction,
Phrase,
Structural,
Symbol,
Predication,
Lexicon
** {} ;
</PRE>
<P></P>
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Author:
Last update: Tue Jan 31 18:15:47 2006
</P>
<P>
Produced by
gfdoc - a rudimentary GF document generator.
(c) Aarne Ranta (<A HREF="mailto:aarne@cs.chalmers.se">aarne@cs.chalmers.se</A>) 2002 under GNU GPL.
</P>
<P>
==
</P>
<PRE>
abstract Multimodal =
Noun,
</PRE>
<P></P>
<P>
Verb,
</P>
<PRE>
Adjective,
Adverb,
Numeral,
</PRE>
<P></P>
<P>
Sentence,
Question,
Relative,
Conjunction,
Phrase,
Tensed,
</P>
<PRE>
Structural,
Demonstrative,
Lexicon
** {} ;
</PRE>
<P></P>
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<P ALIGN="center"><CENTER><H1> The construction of nouns, noun phrases, and determiners</H1>
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<P ALIGN="center"><CENTER><H1> Numerals</H1>
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Author:
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Author:
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Author:
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Author:
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<P ALIGN="center"><CENTER><H1> Phrases and utterances</H1>
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<I>Author: </I><BR>
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<TITLE> A Small Predication Library</TITLE>
</HEAD><BODY BGCOLOR="white" TEXT="black">
<P ALIGN="center"><CENTER><H1> A Small Predication Library</H1>
<FONT SIZE="4">
<I>Author: </I><BR>
Last update: Tue Jan 31 18:15:47 2006
</FONT></CENTER>
<P></P>
<HR NOSHADE SIZE=1>
<P></P>
<UL>
<LI><A HREF="#toc1">A Small Predication Library</A>
<UL>
<LI><A HREF="#toc2">The category of atomic sentences</A>
<LI><A HREF="#toc3">Predication patterns.</A>
<LI><A HREF="#toc4">Individual-valued function applications</A>
<LI><A HREF="#toc5">Families of types</A>
<LI><A HREF="#toc6">Type constructor</A>
</UL>
</UL>
<P></P>
<HR NOSHADE SIZE=1>
<P></P>
<P>
Produced by
gfdoc - a rudimentary GF document generator.
(c) Aarne Ranta (<A HREF="mailto:aarne@cs.chalmers.se">aarne@cs.chalmers.se</A>) 2002 under GNU GPL.
</P>
<A NAME="toc1"></A>
<H1>A Small Predication Library</H1>
<P>
(c) Aarne Ranta 2003-2006 under Gnu GPL.
</P>
<P>
This library is a derived library built on the language-independent Ground
API of resource grammars.
</P>
<PRE>
abstract Predication = Cat ** {
</PRE>
<P></P>
<A NAME="toc2"></A>
<H2>The category of atomic sentences</H2>
<P>
These sentences have both a positive and a negative form
</P>
<PRE>
cat
AS ;
fun
PosAS : AS -&gt; S ;
NegAS : AS -&gt; S ;
</PRE>
<P></P>
<A NAME="toc3"></A>
<H2>Predication patterns.</H2>
<PRE>
predV : V -&gt; NP -&gt; AS ; -- one-place verb: "x converges"
predV2 : V2 -&gt; NP -&gt; NP -&gt; AS ; -- two-place verb: "x intersects y"
predV3 : V3 -&gt; NP-&gt;NP-&gt; NP -&gt; AS; -- three-place verb: "x intersects y at z"
predVColl : V -&gt; NP -&gt; NP -&gt; AS ; -- collective verb: "x and y intersect"
predA : A -&gt; NP -&gt; AS ; -- one-place adjective: "x is even"
predA2 : A2 -&gt; NP -&gt; NP -&gt; AS ; -- two-place adj: "x is divisible by y"
predAComp : A -&gt; NP -&gt; NP -&gt; AS; -- comparative adj: "x is greater than y"
predAColl : A -&gt; NP -&gt; NP -&gt; AS ; -- collective adj: "x and y are parallel"
predN : N -&gt; NP -&gt; AS ; -- one-place noun: "x is a point"
predN2 : N2 -&gt; NP -&gt; NP -&gt; AS ; -- two-place noun: "x is a divisor of y"
predNColl : N -&gt; NP -&gt; NP -&gt; AS ; -- collective noun: "x and y are duals"
predAdv : Adv -&gt; NP -&gt; AS ; -- adverb: "x is inside"
predPrep : Prep -&gt; NP -&gt; NP -&gt; AS ; -- preposition: "x is outside y"
</PRE>
<P></P>
<A NAME="toc4"></A>
<H2>Individual-valued function applications</H2>
<PRE>
appN2 : N2 -&gt; NP -&gt; NP ; -- one-place function: "the successor of x"
appN3 : N3 -&gt; NP -&gt; NP -&gt; NP ; -- two-place function: "the distance from x to y"
appColl : N2 -&gt; NP -&gt; NP -&gt; NP ; -- collective function: "the sum of x and y"
</PRE>
<P></P>
<A NAME="toc5"></A>
<H2>Families of types</H2>
<P>
These are expressed by relational nouns applied to arguments.
</P>
<PRE>
famN2 : N2 -&gt; NP -&gt; CN ; -- one-place family: "divisor of x"
famN3 : N3 -&gt; NP -&gt; NP -&gt; CN ; -- two-place family: "path from x to y"
famColl : N2 -&gt; NP -&gt; NP -&gt; CN ; -- collective family: "path between x and y"
</PRE>
<P></P>
<A NAME="toc6"></A>
<H2>Type constructor</H2>
<P>
This is similar to a family except that the argument is a type.
</P>
<PRE>
typN2 : N2 -&gt; CN -&gt; CN ; -- constructed type: "list of integers"
}
</PRE>
<P></P>
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<P ALIGN="center"><CENTER><H1> Questions and interrogative pronouns</H1>
<FONT SIZE="4">
<I>Author: </I><BR>
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Last update: Tue Jan 31 18:15:45 2006
</FONT></CENTER>
<P></P>

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<P ALIGN="center"><CENTER><H1> Relative clauses and pronouns</H1>
<FONT SIZE="4">
<I>Author: </I><BR>
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<P ALIGN="center"><CENTER><H1> Sentences, clauses, imperatives, and sentential complements</H1>
<FONT SIZE="4">
<I>Author: </I><BR>
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<P ALIGN="center"><CENTER><H1> GF Resource Grammar API for Structural Words</H1>
<FONT SIZE="4">
<I>Author: </I><BR>
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Last update: Tue Jan 31 18:15:45 2006
</FONT></CENTER>
<P></P>

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<P ALIGN="center"><CENTER><H1> Symbolic expressions</H1>
<FONT SIZE="4">
<I>Author: </I><BR>
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</FONT></CENTER>
<P></P>
@@ -16,7 +16,7 @@ Last update: Thu Jan 26 15:05:56 2006
<UL>
<LI><A HREF="#toc1">Symbolic expressions</A>
<UL>
<LI><A HREF="#toc2">Noun phrases with symbols</A>
<LI><A HREF="#toc2">Noun phrases with symbols and numbers</A>
<LI><A HREF="#toc3">Symbol lists</A>
</UL>
</UL>
@@ -36,18 +36,19 @@ gfdoc - a rudimentary GF document generator.
grammar <A HREF="Lang.html">Lang</A>.
</P>
<PRE>
abstract Math = Cat ** {
abstract Symbol = Cat ** {
</PRE>
<P></P>
<A NAME="toc2"></A>
<H2>Noun phrases with symbols</H2>
<H2>Noun phrases with symbols and numbers</H2>
<PRE>
fun
SymbPN : Symb -&gt; PN ; -- x
IntPN : Int -&gt; PN ; -- 27
CNIntNP : CN -&gt; Int -&gt; NP ; -- level 53
CNSymbNP : Det -&gt; CN -&gt; [Symb] -&gt; NP ; -- (the) (2) numbers x and y
SymbPN : Symb -&gt; PN ; -- x
IntPN : Int -&gt; PN ; -- 27
FloatPN : Float -&gt; PN ; -- 3.14159
CNIntNP : CN -&gt; Int -&gt; NP ; -- level 53
CNSymbNP : Det -&gt; CN -&gt; [Symb] -&gt; NP ; -- (the) (2) numbers x and y
</PRE>
<P></P>
<A NAME="toc3"></A>
@@ -70,5 +71,5 @@ This produces <I>x, y and z</I>, in English.
<P></P>
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<P ALIGN="center"><CENTER><H1> Tense, Polarity, and Anteriority</H1>
<FONT SIZE="4">
<I>Author: </I><BR>
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Last update: Tue Jan 31 18:15:46 2006
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<TITLE> Tensed forms of sentences, questions, and relative clauses</TITLE>
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<P ALIGN="center"><CENTER><H1> Tensed forms of sentences, questions, and relative clauses</H1>
<FONT SIZE="4">
<I>Author: </I><BR>
Last update: Wed Jan 25 10:50:14 2006
</FONT></CENTER>
<P></P>
<HR NOSHADE SIZE=1>
<P></P>
<UL>
<LI><A HREF="#toc1">Tensed forms of sentences, questions, and relative clauses</A>
</UL>
<P></P>
<HR NOSHADE SIZE=1>
<P></P>
<P>
Produced by
gfdoc - a rudimentary GF document generator.
(c) Aarne Ranta (<A HREF="mailto:aarne@cs.chalmers.se">aarne@cs.chalmers.se</A>) 2002 under GNU GPL.
</P>
<A NAME="toc1"></A>
<H1>Tensed forms of sentences, questions, and relative clauses</H1>
<P>
This module defines the 2 x 4 x 4 = 16 forms generated by different
combinations of tense, polarity, and
anteriority, which are defined in <A HREF="Tense.html">Tense</A>.
A variant with just the polarity variation is given in
<A HREF="Untensed.html">Untensed</A>.
</P>
<PRE>
abstract Tensed = Cat, Tense ** {
fun
UseCl : Tense -&gt; Ant -&gt; Pol -&gt; Cl -&gt; S ;
UseQCl : Tense -&gt; Ant -&gt; Pol -&gt; QCl -&gt; QS ;
UseRCl : Tense -&gt; Ant -&gt; Pol -&gt; RCl -&gt; RS ;
}
</PRE>
<P></P>
<P>
Examples for English <CODE>S</CODE>:
</P>
<P>
Pres Simul Pos ODir : he sleeps
Pres Simul Neg ODir : he doesn't sleep
Pres Anter Pos ODir : he has slept
Pres Anter Neg ODir : he hasn't slept
Past Simul Pos ODir : he slept
Past Simul Neg ODir : he didn't sleep
Past Anter Pos ODir : he had slept
Past Anter Neg ODir : he hadn't slept
Fut Simul Pos ODir : he will sleep
Fut Simul Neg ODir : he won't sleep
Fut Anter Pos ODir : he will have slept
Fut Anter Neg ODir : he won't have slept
Cond Simul Pos ODir : he would sleep
Cond Simul Neg ODir : he wouldn't sleep
Cond Anter Pos ODir : he would have slept
Cond Anter Neg ODir : he wouldn't have slept
</P>
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<P ALIGN="center"><CENTER><H1> The Reduced Top Module of the Resource Grammar</H1>
<FONT SIZE="4">
<I>Author: </I><BR>
Last update: Fri Jan 20 18:01:40 2006
</FONT></CENTER>
<P></P>
<HR NOSHADE SIZE=1>
<P></P>
<UL>
<LI><A HREF="#toc1">The Reduced Top Module of the Resource Grammar</A>
</UL>
<P></P>
<HR NOSHADE SIZE=1>
<P></P>
<P>
Produced by
gfdoc - a rudimentary GF document generator.
(c) Aarne Ranta (<A HREF="mailto:aarne@cs.chalmers.se">aarne@cs.chalmers.se</A>) 2002 under GNU GPL.
</P>
<A NAME="toc1"></A>
<H1>The Reduced Top Module of the Resource Grammar</H1>
<P>
This grammar is just a collection of the different modules,
and one that can be imported when one wants to test a reduced version
of the grammar. The complete top module is <A HREF="Lang.html">Lang</A>.
The main constructs missing are tenses of sentences, numerals, and
comprehensive lexicon.
</P>
<PRE>
abstract Test =
Noun,
Verb,
Adjective,
Adverb,
Sentence,
Question,
Relative,
Conjunction,
Phrase,
Untensed,
-- Tensed,
-- Structural,
-- Basic,
-- Numeral,
Lex
** {} ;
</PRE>
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<P ALIGN="center"><CENTER><H1> Untensed forms of sentences, questions, and relative clauses</H1>
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<I>Author: </I><BR>
Last update: Fri Jan 20 18:01:40 2006
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<LI><A HREF="#toc1">Untensed forms of sentences, questions, and relative clauses</A>
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Produced by
gfdoc - a rudimentary GF document generator.
(c) Aarne Ranta (<A HREF="mailto:aarne@cs.chalmers.se">aarne@cs.chalmers.se</A>) 2002 under GNU GPL.
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<H1>Untensed forms of sentences, questions, and relative clauses</H1>
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This module defines just positive and negative present tense forms.
Am alternative with full variation in polarity, tense, and anteriority is
given in <A HREF="Untensed.html">Untensed</A>.
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<PRE>
abstract Untensed = Cat ** {
fun
PosCl, NegCl : Cl -&gt; S ;
PosQCl, NegQCl : QCl -&gt; QS ;
PosRCl, NegRCl : RCl -&gt; RS ;
}
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<P ALIGN="center"><CENTER><H1> The construction of verb phrases</H1>
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Last update: Thu Jan 26 15:05:57 2006
Last update: Tue Jan 31 18:15:46 2006
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==Special-purpose APIs==
===Multimodal===
- [Multimodal gfdoc/Multimodal.html]: main module for multimodal dialogue systems
- [Demonstrative gfdoc/Demonstrative.html]: demonstrative noun phrases and adverbs
===Mathematical===
- [Mathematical gfdoc/Mathematical.html]: main module for mathematical language
- [Predication gfdoc/Predication.html]: predication with verbs, adjectives, etc
- [Symbol gfdoc/Symbol.html]: symbols and numbers in text