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

["Jorge Llambías" <jjllambias@gmail.com>]

On Sun, Dec 21, 2008 at 8:15 AM, Pierre Abbat <phma@phma.optus.nu> wrote:
>
> How's this for a definition of the na-rule?:
> 1. Convert all conjunctions that connect two clauses (ijek) or bridi-tails
> (gihek) to forethought.
> 2. Move {na} which is not part of a conjunction as far as possible toward the
> beginning of the sentence without jumping over a conjunction that connects
> two clauses or bridi-tails, and replace it with {naku}.
> e.g. su'oda na broda gi'e brode
> ->su'oda ge na broda gi brode
> ->su'oda ge naku broda gi brode

It looks unambiguous, as far as I can tell. Of course it does maintain
the unintuitive relationship between {su'o da na broda gi'e brode} and
{su'o da na broda}.

> 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}?

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).

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.

mu'o mi'e xorxes


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