Re: Practical effects of all this discussion
phayes@cs.uiuc.edu
Message-id: <199304281946.AA14825@dante.cs.uiuc.edu>
Date: Wed, 28 Apr 1993 14:48:48 +0000
To: interlingua@ISI.EDU
From: phayes@cs.uiuc.edu
X-Sender: phayes@dante.cs.uiuc.edu
Subject: Re: Practical effects of all this discussion
Cc: sowa@turing.pacss.binghamton.edu
John Sowa writes:
>The recent flurry of notes about possible worlds, models, etc.,
>seems to have reached the point where all the discussants (Pat Hayes,
>Len Schubert, Chris Menzel, Jim Fulton, and I) are too exhausted to
>say anything more about the subject.
Sorry, Ive just been away. And I agree that these issues are important,
which is why I want to try to get some points straight.
It is important to get clear that John Sowa has a very idiosyncratic and
singular philosophical position, and not let this be simply accepted as
established fact or dogma. I do not want to argue that his view is wrong -
these are issues on which one can consistently take any of several views,
and debates between them belong in the philosophical literature - but since
the context of this entire discussion is the design of a standard
representational language, it would be unfortunate if that design were to
be unduly influenced by these ideas, especially if their details are not
entirely worked out. Anyone who confidently tosses aside almost a century
of work in the foundations of mathematics should be treated with a certain
amount of caution.
John does seem to misunderstand, and certainly mis-states, some of the
basic ideas of conventional semantics, notably that of a Tarskian model or
interpretation.
Tarskian model theory - TMT - defines how the denotations of symbols
interact to give the denotations of more complex expressions. Thus for
example it says that if we interpret a relation symbol 'Bigger' to refer to
a certain relation between things, and interpret the name 'New York' to
refer to a thing, and 'Arthur' to refer to another, then 'Bigger(Arthur,
NewYork)' is true just if that relation holds between those things; and so
forth. That is all it says, simple things like that. A 'model' of some
collection of symbols is simply a complete specification of appropriate
denotations for them all. This is usually described set-theoretically,
largely because thats the way mathematics is done these days, but that has
no deep significance, and certainly doesnt mean that the models must be
somehow unreal or abstract, or of course that they must be mental
structures or data structures (where on earth did THAT idea come from?)
To emphasise the point, imagine a tiny language with three names 'Arthur',
'Joe' and 'C', and one binary relation name 'Bigger'. Then I might
interpret 'Arthur' to refer to the Queen Elizabeth 2, 'Joe' to refer to my
sister Mary, 'C' to refer to the dirty stain on the window of my office
(assuming of course that these can all be accepted as things) and 'Bigger'
to refer to the relation which holds between physical things when the first
is at least as old as the second. Then 'Bigger(C,Joe)' is false and
'((Forall ?x) (Exists ?y) Bigger(?x,?y))' is true, for example. Now, I just
defined a Tarskian model. The things in its universe were real, not data
structures. To say that it is a 'possible world' is just a way of saying
that it is a possible way to interpret that language in the world. To
insist that there is only one world, does not rule out all kinds of ways of
mapping symbols into it.
TMT does not assume that its models are in any sense complete
specifications of the world. It does assume that quantifiers range over all
the things that are being taken (in this model) to constitute the domain,
and this is an assumption which Situation Theory chose to reject, allowing
essentially partial quantifiers. McCarthy's idea of 'contexts' is another
way of making quantifiers range over part of what is being taken to be the
domain of things. One can argue about the utility or power of these
modifications to TMT, but these arguments have nothing to do with whether
or not the things being quantified over are real.
TMT does assume that the concept of 'thing' is somehow specified, and the
universe of things is specified, and what counts as a relation is
specified. John observes that these specifications might be given in all
sorts of ways: the world does not come with crisp edges to 'things' given
to us, we have to impose them. True, but this makes not a whit of
difference to TMT. It can even be stated as the observation that a given
piece of the world might be used as a TMT interpretation in many ways. It
is merely to observe that TMT assumes that ontological issues are somehow
settled, and makes very few committments in this direction. (It does assume
that names refer to individuals, which is itself not uncontroversial;
readers of this email will no doubt be familiar with the chief alternative,
mereology, which takes expressions to refer to disconnected pieces of a
continuum. An exactly similar debate can be had about whether mereological
models are made of reality or must be mental.)
John also seems to think that (perhaps because TMT is usually phrased in
set-theoretic terms) these things and the relations between them, and so
on, are data structures. This is a much more peculiar idea. On the face of
it is simply wrong, since as I observed in an earlier message, data
structures are finite, but universes need not be (and some, eg the
integers, are usually taken to not be.) John's reaction to this point is to
simply reject all of modern mathematics since Hilbert. This reveals
considerable selfconfidence, but I do not find it very convincing. Most
rebels in mathematical philosophy - even the intuitionists - have agreed
that there are infinitely many integers.
But even if we keep away from mathematics, it is a strange idea. Much of
what we say, and certainly what we want to encode in representation
languages, quite clearly has nothing to do with mental or data structures.
A Kbase might consist of descriptions of the stress patterns in bridge
girders, or the current balances in bank accounts, or the whereabouts of
military units, etc. etc.. None of this is mental structure or data
structure. (Footnote: of course the things in the Kbase ARE data
structures, and my beliefs ARE mental structures, but they REFER to other
kinds of thing.)
It makes sense in one case. If we want to express knowledge about other
knowledge - as in discussing beliefs or reasoning about possible
misunderstandings, for example - then the problem arises of how to describe
these things. If we want to describe them in the same way that we would if
the system itself believed them - so that to represent 'harry believes
...', we can write something with the content 'harry believes this:'...'' -
and if in addition we want to be able to quantify into these quoted
expressions; if all this, then indeed some problems arise with
straightforward TMT, since it is not able to account for the apparent
meaning of the quantifiers in this case. This is now very well understood,
and modal logics handle the resulting compexities quite well. John is
centrally concerned with this case, has philosphical objections to the
modal logic semantics, and wishes to modify the semantics of KIF to make
this case easier. His proposed solution is idiosyncratic and has not been
fully worked out, but in any case is too eccentric for a proposed knowledge
representation standard.
Pat Hayes
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