Simon, John B, David, Rich, and Bruce, (01)
The thread about Barbara P. has split into several topics.
I'll respond under this heading because *every* implementation
of any formal theory of semantics over the past 40 years meets
the definition of a *controlled* NL. (02)
Simon
> Partee can be considered very much a Montagovian at heart;
> the closest counterpart within the generative semantic deviancy
> would be the late Jim McCawley. (03)
I agree with that point and your other comments. I mentioned Lakoff
for two reasons: (1) Barbara P. mentioned him, and (2) I agree with
George L's much harsher criticisms. But unlike George, I believe
that formal semantics is useful for designing and implementing CNLs
 and for some processing of NLs *after* a lot of heuristics have
been used for the hard parts. (04)
But I would apply the word 'deviancy' to Chomsky's truly *weird*
views about language. I believe that Michael Halliday (born in
the same year as Noam C) is far more realistic and useful. For
a review, see http://www.jfsowa.com/pubs/halliday.pdf (05)
John B
> Most of the Reddit discussions pertain to whether Constructed
> Languages [such as Esperanto and Klingon] are really languages.
> ... for me, the overall discussion of Constructed Languages seems
> to touch on Controlled/Constrained Natural Languages. This is
> important, I believe, because we are in for an extended era of
> many CNL's as people partition core and technical vocabularies
> in various ways, trying to satisfy needs for particular disciplines
> and markets. (06)
Yes. All those notations are processed by the same neural mechanisms
as NLs, and people freely embed symbols and phrases from them in their
native NLs. Just look at Lewis Carrol's Jabberwocky. Some of his
invented words have been accepted in English dictionaries. (07)
John B
> My question is whether ConLangs, shorthands and CNL's are entities
> of Chomsky's hierarchy of languages? (08)
Since all versions that anyone has implemented can be serialized
in notations with a formal grammar, they have a position in that
hierarchy. They rarely go beyond the contextsensitive subset. (09)
John B
> My main concern is that while we know how to markup equation,
> we have little understanding of the KR for math. (010)
The formal KR for math is math. The axioms for every version have
been stated by the mathematicians. But I admit that it's not easy
to explain their implications to a nonmathematician. George Polya
did a good job of explaining how mathematicians think about math
and make their discoveries. See (011)
Polya, George (1945) How to Solve It, Princeton: University Press. (012)
Polya, George (1954) Mathematics and Plausible Reasoning, Volume I:
Induction and Analogy in Mathematics, Volume II: Patterns of
Plausible Inference, Princeton: University Press. (013)
David
> The real question in my mind, is whether it is useful to do this.
> It seems that we want pictures to be their own representation. (014)
Yes. But it's useful to have a linear interchange format for
sending them to and from computer systems that process them.
The real understanding is in terms of the imagery. (015)
Rich,
> Math would have to be considered a language. (016)
Yes. Every symbol and phrase in math is a shorthand for some
NL word or phrase. The symbol '+' is a variant of '&', which
is an abbreviation for 'et'. The formula '2 + 2 = 4' is
shorthand for "Two and two is four". (017)
Rich
> Math isn’t speakable like English or German (018)
Au contraire, every mathematical formula can be read in any NL
by expanding the abbreviations. Two mathematicians can discuss
their ideas over the phone. Each of them might use a pencil
and paper as an aid to memory, but that is just a convenience. (019)
Bruce
> What is the mapping between a symbol and the reality it represents?
> I was fascinated by issues in “modeling languages” (how does an
> abstract symbol reliably wrap around reality?), and this question
> is a core issue in testing scientific theory. (020)
That is indeed important. But the mappings for all symbols of
any kind use the same mechanisms of perception, action, and
cognition as the NL used to explain those symbols. (021)
That doesn't solve the problem, but it puts it in the same basket
as the many, many problems about language understanding. (022)
John (023)
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