[lojban] Re: [lojban-beginners] Re: About the negators

[Pierre Abbat <phma@phma.optus.nu>]

On Sunday 21 December 2008 13:53:53 Jorge Llambías wrote:
> On Sun, Dec 21, 2008 at 8:15 AM, Pierre Abbat <phma@phma.optus.nu> wrote:
> > su'oda nage broda gi brode
> > doesn't change, because {na} is part of the conjunction {nage}.
>
> {na} is not really part of the conjunction. Do you mean it is
> equivalent to: {su'o da na ku zo'u ge da broda gi da brode} or to {na
> ku su'o da zo'u ge da broda gi da brode}?

{naku su'oda zo'u ge da broda gi da brode}. I was thinking of {ganai}; in 
{naje}, {na} is part of the conjunction, whereas in {nage}, it isn't.

> A full specification of the rules would go something like this:
>
> We define an "atomic bridi" as a bridi that contains no bridi
> negations, no (outer) quantifiers, and no (logical) connectives. It
> corresponds to an atomic formula of pedicate logic.  (In an atomic
> bridi, the order of arguments can be changed freely with SE and/or FA,
> without changing meaning).

It can contain bridi negations inside a sumti; these aren't affected by the 
transform, unless you apply it to the bridi inside the sumti. e.g. {lo na 
gerku cu batci mi}.

> We define a "well formed bridi" (wfb), corresponding to well formed
> formulas of predicate logic, as follows:
>
> An atomic bridi is a wfb.
> A wfb preceded by {na ku zo'u} is a wfb.
> A wfb preceded by {ro da zo'u} is a wfb. (And the same for the other
> quantifiers.)
> Two wfb connected with {ge .. gi ...} give a wfb. (And the same for
> the other logical connectives.)
> Nothing else is a wfb.
>
> That is all that is required to express the wff's of first-order
> predicate logic, and the logical structure of a wfb is always clear.
> But Lojban provides some additional "shortcut" notations (negations
> and quantifiers moved out of the prenex and into the matrix of the
> bridi, and sumti and bridi-tail connectives) that are always
> equivalent to some wfb. The rules to transform a general bridi into
> wfb form are as follows:
>
> Step 1: write all afterthought connectives in forethought form.
> Step 2: going from left to right:
> (a) when a naku is found in the matrix, move to last place in the
> prenex of current bridi.
> (b) when a quantifier is found in the matrix, move to last place in
> the prenex of current bridi, leaving a copy of the variable in place
> in the matrix.
> (c) when a connective is found, expand to a full bridi connective,
> leaving a copies of the shared terms in each connected bridi (this may
> require introducing some goi ko'a or similar when the shared term is
> not already a variable.)
> (d1) when a na is found, move (as naku) to last place in the prenex of
> current bridi.
> (d2) when a na is found, move (as naku) to first place in the prenex
> of current bridi.
>
> Rule (d1) is what I propose, rule (d2) is what you propose.

In {su'oda na broda gi'e brode}, you have to convert {gi'e} to forethought 
before moving {na}, else it won't find a {ge} to stop it.

This transform also applies to non-logical connectives, although the result 
won't be a logical wfb. E.g.:
ti na gucti li re joi pulgada li so
-> ti joigi na gucti li re gi pulgada li so
-> ti joigi naku gucti li re gi pulgada li so

mu'omi'e pier.


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