The syntax of numbers and number words 1. The External Syntax of Numbers. Post Determiners ---------------- Numbers are post-determiners, whether cardinal, ordinal, or fractions. The hundred old men The three new cups five pencils The hundredth man The fifth pencil The two-thirds cups of flour. It would be tempting to assign number words like "one", "five", "ten", "hundred", "thousand", "million" and their ordinal and denominator forms to that class. But number-words are better regarded as the building blocks of post-determiners. In an expression like "three hundred and fifty-three cups of coffee", "three hundred and fifty-three" is the post-determiner. Agreement for number words -------------------------- A. Cardinal All cardinal numbers determine plural nouns except "one". two men *two man five million three hundred and forty-three men *five million three hundred and forty-three man *one men one man But when one is part of a larger number the number determines a plural noun: five million three hundred and forty-one men *five million three hundred and forty-one man Similarly, when cardinal numbers appear with elided heads number for subject/verb agreement parallels the restrictions noted above. *Three men are found after the crash; two dies. Three men are found after the crash; two die. Three men are found after the crash; one dies. *Three men are found after the crash; one die. The code "agreement=singular;full_cardinal" is added to the entry for "one" to indicate this special behavior. B. Ordinal: Ordinal numbers determine singular nouns: the second man *the second men the three hundred and forty third man *the three hundred and forty third men except "first" which determines both singular and plural nouns: the first man the first men but only when first is a full cardinal number. the three hundred and forty first man *the three hundred and forty first men So the code "agreement=plural;full_ordinal" marks this exceptional behavior. C. Fractions Fractions all determine plural nouns, and in head elided constructions agree as plurals. Only three fifths plates of spinach were eaten. *Only three fifths plate of spinach was eaten. Three men are found, and three fifths die. Three men are found, and three fifths dies. So no lexical agreement= codes are needed to distinguish special behavior. The only lexical record marked with "agreement=" codes is "one": {base=one cat=number_word variant=first;ordinal number_type=unit agreement=singular;full_cardinal agreement=plural;full_ordinal } 2. The Internal Syntax of numbers and number words. Numbers are of three types: Cardinal, Ordinal and Fractional. Each is constructed out of number words. A number word alone (properly inflected) can be a cardinal or ordinal number, but not a fraction. There may be many ways to describe the gammar of these numbers, The grammar below is one attempt. The grammar below descibes the american system and would need modification to cover the British system. A. Cardinal Numbers: First we need lexical classes of number words. Membership in these classes is indicated in the lexical entries for number words in a number_type=slot. "ten" and "hundred" are unique words, each in it's own class, I'll just mention them by name. units= {one,two,three,four,five,six,seven,eight,nine} 1. morphologically simple 2. occur in environment _ hundred Units are marked number_type=unit in the lexicon. teens= {eleven, twelve,thirteen,fourteen,fifteen,sixteen, seventeen, eighteen, nineteen} 1. morphologically: unit+teen 2. occur in envrionment __ hundred Teens are marked "number_type=teen" in the lexicon. decades = {twenty, thirty,forty, fifty, sixty, seventy, eighty, ninety} 1. morphologically unit+ty 2. cannot occur in __ hundred 3. occur in environment __ unit. * ten five * one five twenty five Decades are marked "number_type=decade" in the lexicon. Magnitude words: 1. morphologically: latin number + illion 2. occur in a specified order with respect to each other. *five million ten billion. *six trillion three thousand. Magnitude words are have the lexical code "number_type=magnitude" with an additional slot "power=". When power=N 1000^N is the value. Numbers in the power= slot are also used to maintain the order of magnitude words. Notice that the denotation of these words and their etymology are off by one. Bi-illion is power 3. "hundred" is morphologically different from the other magnitude words but semantically similar. magnitude_word hundred power=0 thousand power=1 million power=2 billion power=3 trillion power=4 quadrillion power=5 quintillion power=6 sextillion power=7 septillion power=8 octillion power=9 nonillion power=10 decillion power=11 undecillion power=12 duodecillion power=13 tredecillion power=14 quattuordecillion power=15 quindecillion power=16 sexdecillion power=17 septendecillion power=18 octodecillion power=19 novemdecillion power=20 vigintillion power=21 centillion power=101 The Grammar: ----------- Some terminology: Basic cardinal numbers represent values less than 100. A cardinal number of rank N (Card_Number(N)) means a cardinal number representing a value between 1,000 to the Nth power and 1,000 to the N+1th power. The cardinal numbers of rank 0 represent numbers in the hundreds. The cardinal numbers of rank 1 are in the thousands and those of rank 2 are in the millions, 3 in the billions etc. Cardinal numbers of rank 21 are in the vigintillions. Card_Number( can be read "consists of". Rules: ________ Rule 1: Basic Cardinal Numbers ------------------------------ Basic_Card_Number ==> {unit, "ten", teen, decade(+("-")+unit)} A basic cardinal number may be a unit alone, a teen alone, the number "ten" or a decade optionally followed by a unit. A dash "-" may occur between the decade and the unit. e.g. five unit ten "ten" twelve teen forty decade twenty five decade+unit forty-six decade+"-"+unit Only decades may be followed by a unit: *ten four *fifteen six Rule 2: Cardinal Numbers of Rank 0 ---------------------------------- Card_Number(0) ==> unit + hundred + ((and) + Basic_Card_Number) A cardinal number of rank 0 consists of a unit or decade+unit followed by "hundred" optionally followed by a basic cardinal number. "and" may optionally occur before the basic cardinal number e.g. five hundred unit+hundred six hundred and seventy unit+hundred+basic cardinal number Since "hundred" is Magnitude(0) this rule can almost be assimilated to the rule schema below. Rule 3: Cardinal Numbers of Rank 1 ---------------------------------- Card_Number(1)==>{teen,decade+unit}+hundred + ((and) + Basic_Card_Number) A cardinal number of rank 1 may consist of the word "hundred" preceded by a teen or decade and unit, optionally followed by a basic cardinal number. The basic cardinal number may be preceded by "and". e.g. twelve hundred teen+hundred twenty five hundred and ten decade+unit+hundred+basic cardinal number The decade must be followed by a unit: *twenty hundred, "ten" cannot precede hundred either: *ten hundred. Since the following rule schema also covers cardinal numbers of rank 1, this rule creates a systematic homonymy among cardinal numbers of rank 1. e.g. fifteen hundred == one thousand five hundred twenty five hundred and six == two thousand five hundred and six Rule schema for Cardinal Numbers of Rank > 0; ___________________________________________ Card_Number(N) ==> Card_Number(<1) + Magnitude(N)-word + ({(and) + Card_Number( 0. A cardinal number of rank N (N>0) consists of a magnitude word of power N preceded by a cardinal number of rank <1 and optionally followed by a cardinal number of rank decade+"="+unit Basic_Card_Number ______|______ | | | decade - unit | | | twenty - three Card_Number(0) ==> unit + hundred + and + Basic_Card_Number Card_Number(0) ________|_______________ | | | | unit hundred and Basic_Card_Number | | | | | | | unit | | | | one hundred and two Card_Number(1) ==> Cardinal_Number(0) + Magnitude(1)-word + Card_Number(0) Card_Number(1) ________________|_______________ | | | Card_Number(0) Magnitude(1)-word Card_Number(0) ________|_________ | ________|__________________ | | | | | | | | | | unit hundred and unit | unit hundred and decade unit | | | | | | | | | | one hundred and two thousand four hundred and fifty six Card_Number(1) ==> teen+hundred+basic cardinal number Cardinal_Number(1) __________|_________________ | | | | teen "hundred" "and" Basic_Card_Number | | | | | | | unit | | | | fifteen hundred and six Card_Number(1) ==> Cardinal_Number(0) + magnitude(1)-word + and + Basic_Card_Number Card_Number(1) _________________|_______________________ | | | | Card_Number(0) Magnitude(1)-word and Basic_Card_Number | | | | basic_number | | | | | | | unit | | unit | | | | one thousand and six B. Ordinal Numbers: Ordinal numbers are identical to cardinal numbers except that the right most number word is in Ordinal form: Cardinal Ordinal one first two second twenty-three twenty-third one thousand and six one thousand and sixth C. Fractions A fraction consists of numerator followed by a denominator. The numberator is just a cardinal number. The denominator is identical to a cardinal number except that its right most number word in in denominator form. In most cases the denominator form is the same as the ordinal form. The exceptions are "one" which has no denominator form, and "two" which has a special full_denominator form when it exhausts the denominator. The rule is: Fraction ==> cardinal(alpha number) + denominator(alpha number) (alpha number) indicates that the when the numerator is a number other than "one" the denominator must be in plural denominator form. one-third two-thirds one five hundred and thirty-second two five hundred and thiry-seconds five thousand three millionths