Date: Thu, 7 Mar 1996 13:18:35 -0500
From: Logical Language Group <lojbab@access.digex.net>
Message-Id: <199603071818.NAA08523@access1.digex.net>
To: sbelknap@uic.edu
Subject: Re:  fuzzy lojban
Cc: cowan@ccil.org, pcliffje@crl.com
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Cowan may venture his opinion on his own, but here is Lojbab's opinion:

>1. Where exactly does it say in the BNF, YACC, Refgrammer, or cmavo
>definitions that crisp logic is being used? I don't see it.

I doubt that you will find it.  I don't think it ever entered my mind to
specify it.

>Other than some
>vague statement that lojban is based on predicate logic, I don't see
>*anywhere* where the set membership and logic functions are specified.

What do you mean by "set membership" and "logic functions"?
Set membership is expressed using the predicate cmima, which is not defined
whether it is "crisp" or "fuzzy" membership, and the non-logical connective
ce and ce'o, and the set-converters lu'i and , I think vu'i (for ordered
sets), the cardinal "mei" which has a place for set members to be enumerated,
and "me/ME".

The only logic function is the truth value abstractor jei, and the logical
connectives, and of course logical negation.

These of course by my own arbitrary definitions of your terms %^)

>2. Is the language specification as to logic membership function ambiguous
>or              merely unspecified? Is this agnosticism in the great fuzzy
>vs. crisp debate intentional? 

Unspecified, and probably unconsidered.

>3. How do we know that lojban logic isn't already fuzzy?
> 

We probably don't, but haven't considered it (unless pc has).

>4. Is <ni> a fuzzifying cmavo? (I first asked this question on 26 May 1995
>in my *first post* regarding fuzzy logic in lojban. This question has never
>been answered!)
> 

It depends on what a "fuzzifying ccmavo" would do.  It might serve that role.
But we are lacking a statement of requirements in order to match them up
with features and potential featyures.

>26 May 1995 Fuzzy Ship of Theseus
>mi cusku dihe
>>If there is no clear meaning for ni, perhaps implementing a rich syntax
>>for describing fuzzy sets with ni would be amusing and/or useful.
>>Perhaps the capability exists but is simply unrecognized.

ni has a well-defined syntax, and a loosely defined semantics indicated
more be example than my definition.  Since we don;t know what capability is
desired, we cannot recognize it.

>5. Would there be any obvious problem to using Max, Min, etc as the logical
>operators for the default set membership function of lojban? (they would
>work in the expected way for both fuzzy and crisp logic)

I have seen no definitions of these functions or what they would be
required to do, so I have no opinion on whether we can or do support them in
Lojban.  They are certainly not explicitly identified as such in current
documentation, since I don;t know what they would be used for.  I assume
that these are something other than the brivla "traji".

>The available material appears to be agnostic as to the fuzziness or
>crispness of lojban grammer. The conn.txt paper could be interpreted as
>specifying crisp membership functions in its description of truth tables,
>etc.

That would certainly have been my assumption, never having seen a truth table
built around anything other than two-valued logic.  But I would presume
that if the predicates being connected were other-than-two-valued, that the
connectives would operate on them in some appropriate manner.  If you want
to specify such a manner, we need to see the requirements.

What Cowan has been calling the "logic paper" is not conn.txt, which is the
"connective paper".  The "logic paper" is 
nobody.txt and describes aspects of quantificational logic, and who knows what
else, since I haven't seen it %^).

I want to reiterate that we have NEVER seen from you a statement of what
you perceive to be the requirtements for coverage of fuzziness in Lojban.
You persist in trying to associate design features with what are to everyone
else, rather nebulously defined concepts.  To get any official recgnition
of fuzziness, we need to know what we are trying to do, and I personally feel
that it would be better to let US try to map requirements to whether and how they are covered in the language, once we understand what it is you are trying
for ("us" being Cowan, pc, myself, and possibly Nick Nicholas now that he
again exists, assuming he has some knowledge of fuzzy logic - he does have
sufficient knowledge of the language to be consulted if he knows the concepts.)
We don't know the problem, and hence cannot comment on any solutions.

I will cite pc's question about requirements for you again:
>Do find out what the fuzzys want.  Possibilities:  
>a) fuzzy set theory: xhas property F to degree 0<=n<=1 (presumably a
>         _melipiny_ modifier on the predicate will do this within the present
>        system, though something fancier may be wanted)  Truth values are
>still         binary here.
>   variant 1 allows modified predicates with different membership curves, 
>        but these correspond to the usual adverbs of intensity "very,"
>"slightly ," 
>        "moderately," and so on, and we have all of those already.
>   the other variants of this seem to be the other positions on the 
>        Guttman scale types and all of them seem to be handable with tanru
>or, perhaps, BAI with numerals
>
>b) fuzzy truth values just require some things permitted in the places
>        where truth values go other than T and F, basically [0,1].  This gets
>        dealt with basically as does the corresponding issue for
>probabilities,         which is taken care of, isn't it?
>   strictly this ought to lead to a whole lot of other connectives than 
>        the usual ones, but I almost never see any of those other ones talked
>        about and they don't usually make much practical sense, so we'll
>cross 
>        that bridge if someone suggests it seriously and demonstrates that
>they         know what they are about -- the issue never arose with
>        probabilities either.
>
>c) fuzzy arithmetic (often mixed up with one or the other of the above -- 
>        as values or as measures)  As far as I can see, this just needs a
>piece         of mex, roughly on  a par with with the signs (- and,
>occasionally, +) 
>        that says "fuzzy number"
>
>I'm sure there are some mixes of these and maybe some whole new levels of
>fuzziness that I have not kept track of, but I don't see much in the way
>of big changes here -- or of satisfying people who want big changes (We
>tamed the Juggernaut!) with practical and adequate solutions. 


lojbab