semantical equivalences

I think a list like this has been started somewhere on the wiki, but I couldn't find it. I only give a few categories and a few examples. Some of these are "official", others semantically obvious and unavoidable, others may be more controversial. Here goes (--greg.):

eks

ko'a V ko'e broda == ko'a broda ijV ko'e broda

• What happens if I use bound variables? do I use one prenex with scope cmavo or do I repeat the same prenex twice?
  • Only one prenex. A better way to put it is gV ko'a broda gi ko'e broda. The prenex remains in front of everything. --xorxes

jeks

• I'm not sure about these, there may be some tanru problems, I don't know what happens to other sumti (x2, x3 etc).

ko'e broda jV brode == ko'e broda ijV ko'e brode

• The book says expansion of tanru jek-connectives doesn't always work. The example given is "la .alis. cu blanu je zdani prenu" != "la .alis. cu blanu prenu .ije la .alis. cu zdani prenu", when the interpretation of the tanru is that alice is a person who lives in houses which are blue (though it seems the "je" would likely be left out in that case anyway).

gadri

lo broda cu brode == da poi broda zo'u da brode

le broda goi ko'a e ko'e cu brode == le pamoi broda goi ko'a cu brode ije le remoi broda goi ko'e cu brode

• This last one is useful for determining whether you want le broda or lei broda

na

da na broda == naku da zo'u da broda

da pu na broda == da na pu broda

noda

noda broda == noda zo'u da broda == naku da zo'u da broda

tense negation (with PU or FAhA)

da punai broda == da na pu broda == naku da zo'u da pu broda

zi'o

ko'e zilPAVbroda == ko'e broda FA zi'o

ko'e broda da .ija ko'e broda noda == ko'e broda zi'o

• This is wrong. The left hand side is a tautology (always true). The right hand side can be true or false depending on the circumstances. --xorxes

ko'e broda zi'o ije ko'e broda noda == ko'e broda na'ebo da

• I'd like to know whether this last one makes any sense. I see zi'o as meaning the second to last : "ko'e broda something maybe". I want to be able to say "ko'e broda definately nothing" while still claiming "ko'e broda zi'o".
  • If ko'e broda noda is true, it can't be true that ko'e broda na'eboda. "Other than something" is just another something. You can say ko'e broda zi'o e noda, just one more syllable. --xorxes

• • • But if "something" is unconstrained, we run out of da ...