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On Sat, Sep 1, 2012 at 5:06 PM, And Rosta <and.rosta@hidden.email> wrote: > Jorge Llambías, On 01/09/2012 20:28: > > > > 4 seems the easiest: > > > > la je nmpda je le nnle mneka le nxle mneka snga > > Twelve(A)& (boys(E): among(E,A)& girls(E): among(E,A)): sing(A) > > > The twelve boys and girls sing. > > Just as "twelve boys" means each of the twelve is a boy, so "twelve boys > and girls" means each of the twelve is a boy or a girl (and that some of the > twelve are boys and some are girls). Yes, I realized that after posting. > The way I'd do this would be with a binary 'union' operator "gV", "gV A B" > = "V is the union of A and B": > > la je nmpda ga le sme nnle le sme nxle snga The problem is that "le sme nnle" and "le sme nxle" are closed formulas, they don't define any sets to union. You need things with a free variable for the union: "ga nnla nxla" = "je ri mnika ja nnli nxli je si mnika nnli si mnika nxli" = "each among A is either boy or girl & some among A is boy & some among A is girl". In general: gV F1 F2 := je ri mnikV ja F1 F2 je si mnikV F1 si mnikV F2 where F1 and F2 are normally expected to both have V as a free variable. > But we want something that will also cover "the girls laughed and sang", > with the meaning "each of the girls laughed or sang, and some of the girls > laughed and some of the girls sang". Would that be > > la nxla ga le sme cmle le sme snga It's simpler: la nxla ga cmla snga gV is a binary operator, but it leaves its variable unbound. > I wonder if the logic would survive if gV were changed to ji: > > la je nmpda ji nnla nxla snga > > la nxla ji cmla snga > > ? I've not thought that through, and domestic duties claim my attention > now. It would only work if the two formulas being joined were required to always have a single free variable, which doesn't seem useful because the gV-formula could be embedded within the scope of other binders. mu'o mi'e xorxes