On Sep 12, 2008, at 1:36 PM, John F. Sowa wrote: (01)
> Pat,
>
> The wording that Matthew used seemed to imply that change
> did not exist. My only reason for the elementary intro
> to calculus was to the make the point you summarized:
>
> PH> Indeed. And of course, change occurs in the real world and
>> is described by both 3-d and 4-d ontologies, but in different
>> ways. This is so obvious that nobody felt any need to say it.
>
> But I certainly agree that nobody in AI mentions Dunn's work,
> primarily because they never heard of it. I happened to read his
> paper in a collection of articles in the IBM library, but Dunn
> himself didn't publish anything further about it or promote it. (02)
Hey, I had heard of it, in fact I know the man personally. And I am
(or once was, at any rate) in AI. But I agree, his work is not as
widely known. (03)
>
>
> PH> It is based on - it actually uses - inferences made in
>> a theory which refers directly to the worlds.
>
> More precisely, it refers to elements of a set of undefined
> entities, which Kripke called 'possible worlds'. (04)
This is a vacuous point. All model theoretic constructions are made up
of "undefined entities" in this sense. They are set-theoretic
constructions because it is a mathematical theory. It would be of
little use if it were not. (05)
> Nothing
> in Kripke semantics would change in the slightest if you
> replaced the set of worlds with a set of integers (or real
> numbers, if you want an uncountable set). Instead of using
> the term 'possible world', Hintikka used the term 'model set',
> which is a set of propositions that describe a world, (06)
Which is a DIFFERENT notion. You are mis-describing the history of
modal semantics here. (07)
> but
> he never said much about the nature of those propositions.
>
> The important contribution that Dunn made was to distinguish
> a subset of those propositions called 'laws' and to derive
> Kripke's accessibility relation from the way the laws vary
> from world to world. (08)
So, apply this 'insight' to temporal descriptions. Possible worlds are
times, here, and the accessibility relation is the time-ordering
relation. What "laws" vary from time to time, and how would someone
reconstruct the time-ordering (past-present-future) from how these
"laws" change? And even if this can be done, what advantages does all
this give over using good old, you know, *times*, things like [4pm on
Friday 12 September 2008] ? (09)
>
> So Kripke's semantics is a *proper subset* of Dunn's semantics. (010)
Wrong as stated, since Dunn's semantics has no constructions
corresponding to Kripkean worlds.
>
> There is *nothing* you can do with Kripke semantics that you
> cannot do in exactly the same way with Dunn's semantics. It
> is false that Kripke's semantics is more usable than Dunn's. (011)
It is not false that it has been widely used where Dunn's has not,
however. And I have never seen any useful observation or insight arise
from Dunn's work that was not already clear in the Kripke framework.
Certainly for the Ontolog forum it is simply misleading to claim all
kinds of advantages for Dunn's work when none of these supposed
advantages have ever been realized in practice, and where there is a
huge body of established results based on the other paradigm. (012)
>
>
> PH> The laws and facts are stated explicitly as sentences in
>> theories using Kripke-style semantics.
>
> False. Kripke only developed his semantics for propositional
> modal logic. None of the axioms, theorems, and proofs stated
> with Kripke's version ever used a single predicate that said
> anything about anything in those worlds. Those worlds were
> undefined points, and the only information about them was the
> accessibility relation that linked those points in a graph. (013)
I said Kripke-STYLE, meaning a semantics which uses possible worlds
explicitly, in contrast to a Dunn-STYLE, which rejects possible worlds
as entities and re-conceptualizes them in a meta-theory of sentential
relationships. Of course a Kripke semantics for a purely modal logic
has no predicates referring to the worlds, because modal logics have
no such predicates. But the point at issue was whether it is useful to
have such possible worlds as entities in a semantic theory for a
language which DOES have such predicates, and the answer is clearly
Yes. Whereas to insist on not referring to possible worlds, because it
is (what? simpler??) to refer instead in a METAlanguage to sets of
SENTENCES, is simply bad ontology engineering. Its like (in fact, it
is literally) saying that instead of using clock times we should
instead refer to sets of propositions that are true at those times. (014)
> PH> Check out any of the hundreds of papers on planning using
>> a situation-calculus style of representation.
>
> Any paper that states plans that mention anything about the
> things and events in any of those worlds leaves Kripke far
> behind. Kripke's semantics cannot handle quantified modal
> logic. (015)
Kripke himself did not consider quantifiers in his original papers,
but the framework extends very directly to quantifiers and has been so
extended by others, as I am sure you know. (016)
> To say anything about anything in a world, you need
> to relate facts and laws (i.e., ontologies) about that world. (017)
To say something about anything, you write sentences which refer to
whatever it is you want to talk about. This applies to 'worlds' as
much as it does to chalk and cheese, and it certainly doesn't require
using Dunn's semantics. (018)
>
> And that is where you need Dunn's semantics. But since the
> people who wrote those papers (019)
What papers, exactly? (020)
> never heard of Dunn's semantics,
> they reinvented a very simplified special case.
>
> In fact, that is why so many of them use the axioms for S5,
> which Lewis and almost everybody else who studied the issues
> admitted is unrealistic. But for people who never heard of
> Dunn's semantics, S5 is the only one they can handle because
> it makes the assumption that all the worlds have exactly
> the same laws (or ontology). That is a great simplification,
> but it makes it hard to relate systems that have different
> ontologies -- i.e., almost all of them. (021)
None of the above bears any relationship to the actual practice that I
was talking about, and as far as I can tell bears very little
relationship to reality at all. Who are the 'so many of them' who use
S5, for example? Can you cite one example of AI planning or applied
ontology using S5? (S4 for temporal reasoning, maybe one or two.) (022)
>
>
> Please look at those papers:
>
> http://www.jfsowa.com/pubs/worlds.pdf
>
> http://www.jfsowa.com/pubs/laws.htm (023)
I have read those papers, and I disagree with their conclusions. (024)
Pat (025)
>
>
> John
>
>
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> (026)
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