How do I make a quantifier-less ordinal determiner?

Question

If I have a cardinal number, the RGL allows me to create a determiner from it with or without a quantifier:

mkDet : Quant -> Card -> Det --these five
mkDet :          Card -> Det --five

If I have an ordinal number, the RGL only allows me to create a determiner from it with a quantifier, not without one:

mkDet : Quant -> Ord -> Det --the fifth

The RGL doesn’t have a function like mkDet : Ord -> Det. In other words, the RGL assumes that if a determiner contains an ordinal, then the determiner must always contain a quantifier as well: “the first...” or “a first...” but never just “first...”. This seems like an unreasonable assumption to me: quantifier-less ordinal determiners are perfectly valid (even if less common) in many languages, including English.

So, what should I do if do want a quantifier-less ordinal determiner (“my son goes to third grade” etc.)? My workaround would be to fake it with an empty Quant, but that makes me feel dirty.

Answer 1

Is it necessary to have it as a determiner? If not, then you can use the Ord -> AP instance of mkAP as follows.

resource ThirdGrade = open SyntaxEng, ParadigmsEng, LexiconEng in {
  oper
    third_Ord : Ord = SyntaxEng.mkOrd (mkNumeral "3") ;
    third_AP : AP = mkAP third_Ord ;
    grade_N : N = mkN "grade" ;

    third_grade_NP : NP = mkNP (mkCN third_AP grade_N) ;
    my_son_NP : NP = mkNP (mkDet i_Pron) (mkN "son") ;
    go_to_V2 : V2 = mkV2 go_V to_Prep ;

    example_S : S = mkS (mkCl my_son_NP go_to_V2 third_grade_NP) ;
}

But if you need it to be a Det, then your solution of making an empty determiner seems like the best way to go.