Sincerely,
Rich Cooper
EnglishLogicKernel.com
Rich AT EnglishLogicKernel DOT com
9 4 9 \ 5 2 5 - 5 7 1 2
John Sowa wrote:
CoSLI> ... the same preposition can have multiple
meanings, and
> such variance must be handled through
either underspecified
> models that can be stretched to particular
situations, or models
> which incorporate multiple disparate
meanings that are assigned
> to terms as a situation invites, or models
that take into account
> vague interpretations in situated contexts.
This is a good summary of the issues. Before any
computational
method can be applied to the problem, it's necessary
to analyze
the reasons for the ambiguity and vagueness.
... the language a speaker uses to describe perception
is only partly determined by the geometry (What is
it?) but also by
the function (What does it do?) and the pragmatics
(Why do we care?).
Furthermore, perception can be extremely
precise. ...
LZ> What is needed for this purpose is the machinery
of fuzzy logic.
> In fuzzy logic, as in natural languages,
everything is or is allowed
> to be graduated, that is, be a matter of
degree.
As I have said many times, fuzzy logic has many useful
applications.
But it does not address the critical issue of relating
a time-varying
three-dimensional geometry to a linear string of words
that a speaker
chooses for a particular function and purpose.
It also neglects the case when, in pursuit of precisiation, by focusing
on getting one interpretation more precise, one ignores the ambiguity, duality,
reciprocity and complexity that language offers. That complexity has
evolved for good reason, not to pass singular interpretations to an improved
estimation method. Fuzzy logic is a useful tool and no more than that.
-Rich
I agree that your "qualitative measure of
proximity" is useful for
many purposes. But much more is needed to
integrate "geometric,
functional and pragmatic features" with
"computational models of
spatial language interpretation."
John
-------- Original Message --------
Subject: [bisc-group] Representation of meaning vs.
precisiation of meaning
Date: Mon, 05 Apr 2010 16:23:38 -0700
From: Lotfi A. Zadeh <zadeh@xxxxxxxxxxxxxxxxx>
To: bisc-group@xxxxxxxxxxxxxxxxxxxxxxx
*********************************************************************
Berkeley
Initiative in Soft Computing (BISC)
*********************************************************************
Dear Members of the BISC Group:
As an issue, representation of
meaning has a position of centrality
in linguistics and computational linguistics. In sharp
contrast,
precisiation of meaning has almost no visibility. Is
there a reason?
To begin with, what is meant by
precisiation of meaning? The word
"precisiation" is not in a dictionary. The
concept of precisiation of
meaning was introduced in my 1978 paper "PRUF--a
meaning representation
language for natural languages," International
Journal on Man-Machine
Studies 10, 395-460, 1978, and my 1984 paper
"Precisiation of meaning
via translation into PRUF," Cognitive Constraints
on Communication, L.
Vaina and J. Hintikka, (eds.), 373-402, Dordrecht: Reidel, 1984,
and
developed further in subsequent papers. Today,
precisiation of meaning
plays a pivotal role in Computing with Words (CW or
CWW). CW is
concerned with computation and reasoning with
information described in a
natural language. As we move further into the age of
automation of
reasoning and decision-making, CW is certain to grow
in visibility and
importance.
A major obstacle to precisiation of
meaning is imprecision of
natural languages. Basically, a natural language is a
system for
describing perceptions. Perceptions are intrinsically
imprecise,
reflecting the bounded ability of human sensory organs
and ultimately
the brain to resolve detail and store information.
Imprecision of
perceptions is passed on to natural languages.
Theories of natural language have
always been based, and continue to
be based, on bivalent logic--a logic which is
intolerant of imprecision
and partiality of truth. For this reason, bivalent
logic--by itself or
in combination with probability theory--is not the
right logic for
dealing with imprecision of meaning.
What is needed for this purpose is
the machinery of fuzzy logic. In
fuzzy logic, as in natural languages, everything is or
is allowed to be
graduated, that is, be a matter of degree.
Bivalent-logic-based theories
are intrinsically unsuited for addressing the issue of
graduation. This
explains why precisiation of meaning has almost no
visibility within
linguistics and computational linguistics.
Viewed as an operation, the domain
of precisiation consists of
semantic entities such as propositions, predicates,
questions and
commands. In the following, attention is focused on
precisiation of
propositions and predicates.
Let p be a semantic entity.
Precisiation of p transforms p into a
proposition, p*, which is a mathematically
well-defined computational
model of p. p and p* will be referred to as the
precisiend and
precisiand, respectively. A basic metric of
precisiation is cointension.
Cointension is a qualitative measure of the proximity
of p and p*. High
cointension is associated with close proximity. Thus,
precisiation is
cointensive if p and p* are in close proximity, in
which case p* is a
cointensive model of p. Cointension may be viewed as a
desideratum of
precisiation. Unless stated to the contrary,
precisiation is assumed to
be cointensive.
As a model of p, p* is assumed to
be described in a modeling
(modelization) language, PL. Examples of PL are the
language of
predicate logic, the language of fuzzy logic, the
language of
differential equations, the language of probability
theory, and their
combinations. p is precisiable with respect to PL if
through the use of
PL it is possible to construct a cointensive model,
p*, of p. p is
precisiable if there exists a precisiation language,
PL, with respect to
which p is precisiable. Not every proposition is precisiable.
Representation of meaning of p may
be viewed as a step toward
precisiation of meaning of p. As a simple example,
consider the
proposition p: Vera is middle-aged. The meaning of p
may be represented
as: Age(Vera) is middle-age. The meaning of p is
precisiated by defining
middle-age as a fuzzy set, more specifically, as a
trapezoidal fuzzy
set. In this perspective, as was pointed out already,
representation may
be viewed as an intermediate stage of precisiation. It
is the move from
representation to precisiation that requires the use
of fuzzy logic. To
substantiate this claim, I should like to pose two
simple problems to
members of the BISC Group. Please use your favorite
meaning
representation system, be it semantic networks, Sowa's
conceptual
graphs, predicate logic, FrameNet, etc. to come up
with solutions.
Problem 1. Precisiate p: Carol
lives in a small city near San
Francisco, with the understanding that this
information would be used to
come up with an answer to the question: How far is
Carol from Berkeley?
Problem 2. Precisiate p: Most
Swedes are tall, with the
understanding that this information will be used to
answer the question:
What is the average height of Swedes? CW-based
solutions will be posted
at a later point.
Regards to all.
Lotfi