In keeping with my own suggestion of limiting notes to one per day,
here is my combined responses to various notes of January 25 and 26: (01)
RS> FYI the online tutorial link is broken in your Tarski paper
> referenced above. (02)
Sorry. Following is the brief summary of model theory in
Section 13 of my tutorial on math and logic: (03)
http://www.jfsowa.com/logic/math.htm#Model
Model Theory (04)
PC> John Sowa has told us that he uses a combination of techniques
> to solve knotty problems efficiently. I believe that is what
> will be very effective in general, but for that to work outside
> the confines of a single group – i.e. to enable multiple separately
> developed agents to cooperate in solving a problem- they will also
> need a common language to accurately communicate information. (05)
Thanks for the note, but I would just add that it is not necessary
for *all* agents to agree on a single language for the group.
For example, a group of people who speak multiple languages can
collaborate as long as any two who work together have a common
language or can find a third to act as a translator. (06)
As a computer example, a Java program that controls the user interface
might call a C program for high-speed computation, a Prolog program
for complex AI processing, a relational DB that uses SQL, and an RDF
processor for some data from the WWW. (07)
The way that we implement the idea at VivoMind is based on a paper
I wrote in 2002 about the Flexible Modular Framework (FMF): (08)
http://www.jfsowa.com/pubs/arch.htm
Architectures for Intelligent Systems (09)
The basic principle is that agents are allowed to use any language
whatever to send messages from one agent to another, but one field
of each message identifies the language in which it is written. (010)
In one application of the VivoMind software, we were asked to
process a language other than English. As a quick fix to the
software, we took an off-the-shelf translation package, put a
wrapper around it to make it behave like an FMF agent, and routed
messages through it to translate messages from language X to English.
(A better solution would be to adapt our software to language X, but
this method worked for the prototype, and it was easy to implement.) (011)
FK>> This is what MT people do not seem to understand, because they
> believe in Frege who says that the sense of a sentence is derived
> from the sense of its constituents (words). (012)
DE> I'm not clear on what you're saying here. "Frege" conveys
> no information or context for me. (013)
The principle of *compositionality*, usually attributed to Frege,
is that the meaning of a sentence is derived from the meaning of
each word plus the meaning contributed by the way the words are
put together (the syntax). (014)
For formal languages, such as most versions of logic and programming
languages, this principle is either (a) almost true or (b) true with
qualifications. The primary qualification must address the fact that
the meaning of a statement such as (015)
x = a + b; (016)
depends critically on the datatypes of the variables, which are
specified elsewhere in the program. There are two ways of making
Frege's principle true: (017)
1. Say that the entire program is the unit of compilation (or
sentence, in Frege's sense). Therefore, the full semantics
is accommodated by an analysis of that "sentence". (018)
2. Implement a "symbol table", which contains all the information
about each symbol that has been found in the program. When the
declaration of the each variable is found, an entry for that
variable is placed in the symbol table that specifies its
"meaning". When the statement "x = a + b;" is encountered,
the meaning of the statement is derived from the syntax of
the statement plus the *current* meaning of each symbol as
specified in the symbol table. (019)
For natural languages, many people have tried to apply some
version of principle #2, but the kinds of exceptions that
must be accommodated are enormous and often unpredictable. (020)
For example, one speaker was giving a lecture about the fact
that two negations can make an affirmative, but there is no
language in which two affirmatives can make a negation.
Whereupon, somebody in the back of the room said in a
sarcastic tone of voice: "Yeah, yeah." (021)
DE> What I'm GUESSING you're saying is what I think is a significant
> divide in the MT (machine translation) community. (022)
Actually, everybody in the MT community is well aware of the many
kinds of exceptions, but some people go to great lengths to find
ingenious ways of adapting principle #2 to make Frege infallible.
My answer to those people is "Yeah, yeah." (023)
RF> Your [Pat H's] enormous stream-of-consciousness lists of
> quibbles with every word or phrase make it difficult to keep
> volume down on the list. (024)
Pat's remarks are based on a solid foundation in logic and
computer science, and he was trying to educate the readers of
this list about the importance of keeping the ideas straight.
They are much more than mere quibbles. (025)
As one example, I made the point that pure mathematics differs
from the other sciences because it does not make any statements
or claims about the physical world. The basic methods of
mathematics have not changed since our stone age ancestors: (026)
1. Adopt some rules or axioms that define abstract patterns
(e.g., the numbers, geometrical forms, etc.). (027)
2. Use those rules to generate examples of those patterns.
The stone age rules are to count on your fingers or make
notches on a stick. These are observations, but they
are not observations of physical phenomena. (028)
3. Analyze them to determine the possible range of patterns.
This kind of analysis is usually called a proof. Formal
proofs were codified by Euclid, but the stone age people
who built Stonehenge showed a high degree of sophistication.
They probably used some informal methods of analysis. (029)
The use of rules to generate examples could be called 'empirical',
but Chaitin added the prefix 'quasi-' because those patterns were
generated by mental processes, not by physical mechanisms. That
is much more than a quibble. (030)
RF> It is to John's credit that he is one of the very few people
> who consistently push this problem [about uncertainty]. (031)
Thanks for the acknowledgment. (032)
In academic circles, there are two kinds of people: those who
narrow their focus to precisely delimited problems that they can
formulate clearly and solve in a carefully written publication;
and those who venture into uncharted territory and come back
with exciting, but incomplete surveys of the wilderness. (033)
Both kinds of work are valuable. People who narrow the focus
systematize the field and clarify the foundations. The ones
who march into the wilderness broaden the field and open up
new territory. (034)
We need both kinds. (035)
John Sowa (036)
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