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          16 Jun 90 14:15 EDT
From: cbmvax!uunet!math.ucla.edu!jimc
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To: snark!lojban-list
Subject: Comments on Negation (longer :-(
Date: Wed, 13 Jun 90 17:14:31 -0700
Resent-Date:  Tue, 9 Jul 91 16:23:57 EDT
Resent-To: John Cowan <cowan@snark.thyrsus.com>
Status: RO

 The negation paper is very complete, and there are several features
discussed in it that I will want to add to -gua!spi.  Most of my comments
are not show-stoppers, but problems with various interpretations.

1.  Scales

The distinction made in the paper between "contradictory negation" and
"selbri negation" is very important.  Most (all?) selbri can be
interpreted as specifying a scale, but only for a few gismu are there
matching gismu for opposite scale ends (e.g. light/dark, happy/sad). 
The "polar opposite" cmavo is very useful to build new meanings, which
should be interpreted as an affirmation of the opposite relation,
rather than as a (logical) negation.  

One useful feature in -gua!spi that I didn't see in the paper was a
"central opposite" cmavo which produces the neutral point on the scale.
For example, the centralization of any color scale would be gray;
"happy" would to to "bored" rather than "sad", and so on.  I have found
it useful to apply it also to central properties so that the central
opposite of "level" is "tilted", "fresh" becomes "spoiled", and so on. 

("Fresh" being defined as "undamaged by age or use", it is clearly the
neutral point of an unsigned scale rather than the end of a signed
scale.  Unsigned scales are less common than signed scales. This one
has "rotten" for its periphery.)

In indicators I would be happer to see the prefix, tight-binding na'e
of selbri negation rather than the trailing nai which is used in
logical connectives as a logical (contradictory) word.  Also, you would
have to count words in actual text, but I'll bet you find that na'e
(selbri negation) is a lot more common than na (contradictory).  That's
true in -gua!spi.  And that's a motivation to exchange the words: two
(English) syllables for one.  As for grammar, I had good luck in Nalgol
by sticking the selbri negator in the same grameme with conversions,
since it binds similarly and occupies the same sites.  A selbri-negated
or converted modal operator is allowed, isn't it?  You get neat
meanings this way, interpreting them as abbreviations for a subordinate
clause with the selbri equally converted or negated.  

As a matter of fact, why not let the indicator intensity cmavo apply to
any selbri (I prefer the prefix position) to get the scale center?  In
other words, merge the indicator and selbri syntax, and interpret an
indicator as an abbreviation for a subordinate clause with its selbri
equally negated and intensified.  

2.  Negation of sumti

I'm not too comfortable with using na, a raw contradictory negation,
with an argument (sumti) predicate (selbri).  Here's how I interpret an
argument; see how close it comes to current Lojban doctrine.  Identify
the first case after conversion of the selbri, and stick a placeholder
there.  The selbri is the symbol for a relation, that is, a set of
lists of case occupants.  When there are sub-arguments (including
modal), retain only members which have a referent of those subarguments
in the right cases.  Now make up a set from the case occupants of the
placeholder case.  This is the full referent set of the argument.  Pick
a subset according to the article, and those are the referents of the
sumti.  

For example, try "eater of cheese".  The placeholder goes in X1 (if in X2
the referents would be "foods").  The relation "eat" is here enumerated:
	X1		X2
1.	The rat		My cookies
2.	The rat		My cheese
3.	Me		My cheese
4.	My kid		An apple
	etc.
 Due to the sub-argument, members 1,4 are thrown out and 2,3 remain
(plus possibly some others among the etc.)  Now the case occupants over
the placeholder are "the rat" and "me", and this set is the full
referent set of the sumti -- what would be passed through if the
article were "all".  

Now what is a "non-eater of cheese"?  We've decided that selbri
negation isn't right.  The correct interpretation involves some kind of
complementation -- either those X1's who eat other than cheese (i.e.
all members of the "eat" referent set other than lines 2,3), or the
complement (relative to some universe of discourse) of {"the rat",
"me"}.  I incline toward the second choice since had the first been
wanted, the complementation operator would have been put on "cheese".  

Clearly if the referent set of a sumti is a set, the referent set of
its negation must be derived by complementation.  But I'm not able to
say authoritatively what the universe of discourse should be.  

3.  Existential failure and bogus assertions of existence

I learned (after much agony) that an assertion about all the members of
the null set is true.  St. Anselm's Ontological Proof of the Existence
of God is the most famous example.  Here's a more mundane one.  Let
"the king" mean "the current king of France" which, as a set, is void. 
"All cats have hair" may or may not be true.  Each of the following
propositions is equivalent to each other:

(The king has hair) and (all cats have hair) 
- --Union of arguments in extension--
(The king -union- all cats) have hair
- --Compare argument to "all cats"--
All cats have hair

(For all Q: (P and Q) = Q) implies (P = .TRUE.)  Thus (generalizing
outrageously over the involved predicate), "the king has hair" is
proven true. QED.  (Also, "the king is bald" is true.)

The footnote (6) that use of "lo" constitutes some kind of assertion
that something exists:  I don't see how this can be.  I see this
interpretation instead:  "lo nolraitru" is a sumti with a referent set.
"Lo" means (among other things) that referents must fit the selbri, and
the quantity of such referents turns out to be zero.  Thus an assertion
is made about the members of the null set, but I don't see any
assertion about whether any king of France exists.  To make such, you
would have to put on a subordinate clause (assertion type, not
restriction) with a numeric predicate, stating that more than zero
members were present.  (By the way, I find it very useful to quantify
with zero to make a negative statement, as you mention.)

As to what quantifiers mean:  My feeling is that before the article (no
lo nolraitru) it means to take a subset with that count, selection
in-mind.  After the article (lo no nolraitru) it's a "subordinate
comment": not restrictive, but not exactly a real assertion either. 
It's there to help the listener identify the referents (in this case by
clarifing the count).  If the referents fail to match the comment the
speaker has been unhelpful, but has not made an assertion that can be
denied, particularly with "le" (in-mind selection).  Subordinate
comments have turned out to be quite important in -gua!spi, and are
about equally common as restrictive clauses and subordinate assertions.

4.  Explicit scales

The machinery for explicitly specifying a scale is good to have.  I
shall have to make sure that -gua!spi expresses scales efficiently. 
The concept reminds me of how dimensioned quantitites are specified:
you assert that an argument is on the scale (i.e. "I am heavy") and
then put on a restrictive subordinate clause asserting that the main
bridi is a member of an equivalence class of things with a particular
measure ("70 kilos").  I believe this model works equally well for non-
numeric dimensions:  "The chair is colored" restricted by "main bridi
is in the `red' equivalence class of colored events".  The problem is
that we are used to saying "the chair is red" and implying the scale;
I'm not sure if that's viable under the scale/restriction model, and if
not, whether it's then unreasonable to demand that the
scale/restriction model be used.

5.  Negation of Bizarre Gramemes

I think logically connected abstractions are ridiculous.  This is
better: One abstraction word "nu" means "X1 is an event in the referent
set of the following relation (bridi)".  For "degree/quantity" you have
(already) a gismu whose X2 is an abstraction, and similarly for
"property", and an identity transformation for "event".  You use
internal selbri conjunction (on a shared X2 argument) for your
abstraction conjunctions, and similarly for negation.  It's ridiculous
to try to make ellipsis possible in every corner of the grammar; you
have to use selbri as the foundation of meaning, and then make various
efficiency hacks that are interpreted as abbreviations of clauses. 
Then the wierd and wonderful concepts like connected or negated
abstractions are easily handled at the selbri level, outside the
grammar, and not only that, arbitrary extensions to the category (here,
abstractions) are possible without grammar hacks; the speakers just use
existing gismu creatively in the clause form.

6.  go'i

Go'i (previous sentence anaphor): I agree with your analysis that all
material (specifically negation) on go'i replaces matching material in
the antecedent, or supplements if no match.  The final sentence (section
15) brings up a problem:  just what is the antecedent of go'i?  In -gua!spi
I define it as the previous sentence said by the current listener, which
seems to be the sense used here.  Also, when a connected sentence is the
antecedent what do you do?  (Cry!)

James F. Carter        (213) 825-2897
UCLA-Mathnet;  6221 MSA; 405 Hilgard Ave.; Los Angeles, CA, USA  90024-1555
Internet: jimc@math.ucla.edu            BITNET: jimc%math.ucla.edu@INTERBIT
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