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