## 16.5. Dropping the prenex

It isn't really necessary for every Lojban bridi involving variables to have a prenex on the front. In fact, none of the examples we've seen so far required prenexes at all! The rule for dropping the prenex is simple: if the variables appear in the same order within the bridi as they did in the prenex, then the prenex is superfluous. However, any ro or poi appearing in the prenex must be transferred to the first occurrence of the variable in the main part of the bridi. Thus, Example 16.9 becomes just:

Example 16.25.

 da viska mi There-is-an-X-which sees me.
 Something sees me.

and Example 16.23 becomes:

Example 16.26.

 ro da poi gerku cu vasxu For-every X which is-a-dog, it-breathes.
 Every dog breathes.

You might well suppose, then, that the purpose of the prenex is to allow the variables in it to appear in a different order than the bridi order, and that would be correct. Consider

Example 16.27.

 ro da poi prenu ku'o de For-every X which is-a-person, there-is-a-Y
 poi gerku ku'o zo'u de batci da which is-a-dog : Y bites X.

The prenex of Example 16.27 is like that of Example 16.18 (but with relative clauses): it notes that the following bridi is true of every person with respect to some dog, not necessarily the same dog for each. But in the main bridi part, the de appears before the da. Therefore, the true translation is

Example 16.28.

Every person is bitten by some dog (or other).

If we tried to omit the prenex and move the ro and the relative clauses into the main bridi, we would get:

Example 16.29.

 de poi gerku cu batci ro da poi prenu There-is-a-Y which is-a-dog which-bites every X which is-a-person
 Some dog bites everyone.

which has the structure of Example 16.19: it says that there is a dog (call him Fido) who bites, has bitten, or will bite every person that has ever existed! We can safely rule out Fido's existence, and say that Example 16.29 is false, while agreeing to Example 16.27.

Even so, Example 16.27 is most probably false, since some people never experience dogbite. Examples like 5.3 and 4.4 (might there be some dogs which never have breathed, because they died as embryos?) indicate the danger in Lojban of universal claims even when restricted. In English we are prone to say that Everyone says or that Everybody does or that Everything is when in fact there are obvious counterexamples which we are ignoring for the sake of making a rhetorical point. Such statements are plain falsehoods in Lojban, unless saved by a context (such as tense) which implicitly restricts them.

How can we express Example 16.27 in Lojban without a prenex? Since it is the order in which variables appear that matters, we can say:

Example 16.30.

 ro da poi prenu cu se batci de poi gerku Every X which is-a-person is-bitten-by some-Y which is-a-dog.

using the conversion operator se (explained in Section 5.11) to change the selbri batci (bites) into se batci (is bitten by). The translation given in Example 16.28 uses the corresponding strategy in English, since English does not have prenexes (except in strained logician's English). This implies that a sentence with both a universal and an existential variable can't be freely converted with se; one must be careful to preserve the order of the variables.

If a variable occurs more than once, then any ro or poi decorations are moved only to the first occurrence of the variable when the prenex is dropped. For example,

Example 16.31.

 di poi prenu zo'u There-is-a-Z which is-a-person :
 ti xarci di di this-thing is-a-weapon for-use-against-Z by-Z
 This is a weapon for someone to use against himself/herself.

(in which di is used rather than da just for variety) loses its prenex as follows:

Example 16.32.

 ti xarci di poi prenu ku'o di This-thing is-a-weapon-for-use-against some-Z which is-a-person by-Z.

As the examples in this section show, dropping the prenex makes for terseness of expression often even greater than that of English (Lojban is meant to be an unambiguous language, not necessarily a terse or verbose one), provided the rules are observed.