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Wiki page Reduced logical form changed


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xorxes:

> sentence = selbri [fa sumti ...] /VAU/
> | NA KU ZOhU sentence
> | tag /KU/ ZOhU sentence
> | tag sumti ZUhU sentence
> | quantifier DA
> relative-clauses ZOhU sentence
> | gek sentence gik sentence
>
>
> selbri = Any untagged and unnegated selbri
> (selbri-2 in the EBNF grammar)
>
> sumti = Any unquantified sumti (sumti-6 in
> the EBNF grammar)
>
> tag = tag in the EBNF grammar
>
> gek = gek in the EBNF grammar
>
> gik = gik in the EBNF grammar
>
> (DA are da, de, di and any additional indexed
> variables as needed)
>
> The above grammar is a sub-grammar of the
> Lojban grammar. By that I mean that every
> sentence it generates is a valid sentence of
> the Lojban grammar. I contend that every Lojban
> sentence has a corresponding reduced logical
> form generated from this grammar.

Ah, the LoCCan use of words!. "Reduced" here
applies, I suppose, the dropping the "logically
irrelevant" bits; for the most part sentences are
expanded to get these forms (prenexing requires
anaphora, forethought connectives are regularly
longer than afterthought and shifting to
sentential requires repetitions). Terminology
aside, however, this seems a useful thing to do
for a logical language, moving toward (or away
from, since this is likely a deeper structure
grammar than the usual one — or so a logically
corrupted linguist would say) the form suited for
usual logical applications. The contention is the
usual (ultimately unsupported — in natural
languages) assumption of applied formalized
logics.

>The idea is
> simple: to get the reduced logical form
> eliminate indicators and free modifiers, move
> quantifiers and negations to the prenex, expand
> all logical connectives to forethought sentence
> connectives and finally move all the arguments
> behind the selbri.

For the real deep logical sturcture, it would be
good to get the modals etc. out to the front as
well. This is somewhat problematic, since the
modals (including tense/aspect and mood)is not
grammatically, but only lexically, specifiable.
And there may be cases where this brings to light
ambiguities — in the speaker's intentions,
though maybe not in the Lojban text (details of
the relative placement of tense, mode, negation
and quantification which cannot be dealt with in
the narrow confines of the preselbri slot). The
use of forethought connectives is tidy though not
essential, as is the shift to VSO order.
The devil is, of course, in
> the details. I intend to work out an algorithm
> for producing the reduced logical form for any
> Lojban sentence. (In fact I think there are a
> couple of tricky places where it may not be
> doable, but at least this will show what they
> are.)

As noted, the history of doing this with natural
languages shows that there seem to be intractable
points, readily solved by human intervention but
not algorithmable. They are not generally the
logically interesting cases,though — since where
they are differs from language to language --
sometimes they are crucial. Human intervention,
alas, raises the possibility of special pleading
-- doing the regimentation in a certain way to
justify a certain (predetermined) result rather
than for objective reasons, so it is to be used
very sparingly.

The purpose of this exercise is to
> clarify the argument for the scope of NA. In
> the reduced logical form the relative scopes of
> the different operators are fairly obvious.

The relative scope in each case is just
everything after it in the same sentence (which
is also rather better defined in this
representation).

Is this all about the issue — which has been
around since the beginning of Loglan — of where
sentential negation goes? It is clear, of
course, in prenex form — though in the shift to
forethought connectives some problems could
reappear if {nagi} is allows from {na.a} etc.
(e.g. "only if" for conditionals). I suppose
that, if we shifted everything to "reduced" form,
some rules would be clearer but that does not
solve the issue of where negation goes in
colloquial usage — the issue that has come up
over and over. The prenex position is logically
desirable, but sociolinguistically someplace
close to the verb (after it in VSO and VOS
formats typically, and frequently also in --V)is
the norm. It is not clear why this is the case,
but it seems to be a powerful tendency, hard to
get people to change from. I suppose that is whay
it is retained in Loglan and then in Lojban, even
with all the probolems it generates in other
respects.

 


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