Re: EDI with real semantics
phayes@cs.uiuc.edu (Pat Hayes)
Date: Fri, 26 Aug 1994 13:59:08 -0500
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To: nitin@sybase.com (Nitin Borwankar)
From: phayes@cs.uiuc.edu (Pat Hayes)
Subject: Re: EDI with real semantics
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Hi Nitin
You exhibit the passion which is strangely familiar in many who have
'discovered' fuzzy logic. While fuzzy logic is an interesting and probably
useful notion, the world of ideas should not be divided into the stark
two-valued us-vs-the rest that Fuzzers, ironically, often seem to assume.
Before I respond to some of the issues you raise, let me gently reprove you
for your use of the rhetorical device by which you identify Fuzz with
down-to-earth practicality and Non-Fuzz with academic airyfairiness, citing
the Japanese fuzzy controllers. First, the utility of many-valued - not
necessarily fuzzy - reasoning in adaptive controllers for nonlinear systems
has been well known for about two decades. The commercial fuss made
recently by the Japanese manufacturers should therefore not be identifed
with some kind of fuzzy-fuelled triumph of commerce over academia. Second,
recent work has shown that fuzzy logic is often *not*, in fact, the most
effective many-valued vehicle for adaptive control, but that somewhat
simpler discrete many-valued logics lead to more rapid convergence to a
stable behavior. The ways of research may sometimes seem slow, but they
have a way of uncovering the truth, even in the face of enthusiastic
opinion.
Now let me turn to your central point, which seems to be the need to handle
ambiguity and doubt. Of course this is correct; but ordinary logic can
also, indeed must also, express ambiguity and doubt. Every time one writes
a disjunction (or, equivalently, negates a conjunction) or an existential
quantifier, such doubt is expressed. A collection of axioms does not
usually completely define the meaning of the symbols occurring in it, so
'ambiguity' is present. Take the example you give of a "big and tall"
store. What can be said about 'tall'? Well, most people aren't tall; tall
people have special needs in their clothing. Some tall people are sensitive
about their height and do not wish to be reminded of it, others, especially
men, are proud of it. Tall people can see further than short people but
have more trouble getting into small spaces such as airline seats. And so
on and on. My point here is just that this can all be done WITHOUT EVER
SPECIFYING WHERE THE BOUNDARIES OF TALLNESS ARE. The standard semantic
theory for logic says that in a particular interpretation, indeed, 'tall'
must denote a particular predicate; but there may be many different
interpretations, and in each one the denotation may differ somewhat. So it
is most important not to conclude that because the logic must be strictly
interpreted in any particular interpretation, its MEANING therefore must be
'strict'.
In fact, I find the use of fuzzy logic an odd approach to this (admittedly
complex) issue, since it requires one to make even more extraordinary
arbitrary decisions. A Fuzzer has to specify not just at what height 'tall'
becomes tall,
but an entire spectrum of heights-and-truthvalues regarding the concept.
Perhaps
someone is not tall at 5'6" but begins to be just a bit tall - say, 0.1
tall - at 5'7" and then is 0.3 tall at 6'0" and by the time we get to 6'6"
is 0.95 tall, and so on. Should these truth-spectra be piecewise linear, or
smooth? Do they have differentials? And so on. Far from simplifying things,
fuzzy logic introduces a huge area of unnecessary complexity. Two
two-valued folk might argue about just where 'tall' starts, but two Fuzzers
have an uncountable infinity of things to arbitrarily disagree about.
>How do all these AI/Knowledge based schemes deal with meta-data about
>*information as a product*, if at all ? I suspect - not at all.
>Information-as-a-prodcut is increasingly becoming a larger segment
>of the ( US ) economy.
>How will these structured information-as-a-prodcut transactions
>be modelled in the knowlede based schemes ? Or is the knowledge only
>about transactions involving concrete "things".
Well, I know of no convincing axiomatisation of 'information as a
product',but the best one so far is probably John McCarthys old
formalisation of beliefs. KIF certainly allows the description of
expressions as first-class objects, so there seems to be no a priori
barrier to attempting such a formalisation in KIF. This has nothing
whatever to do with fuzziness, of course.
>If it is based on first-order logic it will suffer from all the
>problems associated with combinatorial explosion for rule based systems
>in real world AI applications. Performance of such systems - time to
>process rules - will always be an issue.
A valid observation, but of course it applies even more strongly to systems
which try to perform deduction in fuzzy logic. There is nothing magic about
fuzzy logic: it is one among a wide spectrum of approaches to multivalued
logic all of which have roughly the same computational properties.
Deduction in any logic with quantifiers leads to large computational search
spaces, and the resulting techniques which have been evolved to handle
these searches are pretty much orthogonal to the detailed nature of the
truth-functions in the logic. Fuzzy logic is singled out not by its actual
properties, but by the almost messainic behavior of the community which has
grown up around it, like a fundamentalist church. It is about equally
fanatical and resistant to (pardon the pun) logical discussion.
>"A *and* not-A" is not allowed in first-order logic.
>Implementers will make possibly ad-hoc judgements on how to resolve
>conflict thus creating inconsistent world-views.
Ah now, this is more intersting. Indeed contradiction is a special state in
conventional logic, but so it is also in fuzzy logic. (The only logics I
know of which, as it were, celebrate contradiction are some very peculiar
logics which were developed to ease the task of making sense of the
Copenhagen interpretation of quantum theory, an area I recommend keeping
ones business thinking well clear of.) This is not surprising when you
consider that drawing a conclusion and finding a contradiction are
essentially the same task. A follows from B just when (B & notA) is
contradictory. This identity is very basic, and runs through almost all
logics, certainly all truthfunctional logics no matter how complex their
truthvalue patterns. (The possible exceptions are nonmonotonic logics, but
fuzzyness is quite monotonic.) You present this as a problem for two-valued
logic as though the logic were obliged to somehow *committ* itself to one
branch or the other of the contradiction; but that isnt how it works at
all. The process of resolving conflict IS the process of drawing a
conclusion. The arbitrariness you speak of is always present in any logic,
since if the logic says you can infer B from A, then you always have th
equally valid logical alternative of inferring not-A from not-B. But this
is the distinction between what you are taking as an assumption and what
you are asking questions about, and this must be determined not by the
logic but by other pragmatic considerations.
Anyway, in brief: be a bit more cynical about the preachings of the church
of Zadeh.
Best wishes
Pat Hayes
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