Pat, (01)
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: (02)
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. (03)
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. (04)
PH> It is based on - it actually uses - inferences made in
> a theory which refers directly to the worlds. (05)
More precisely, it refers to elements of a set of undefined
entities, which Kripke called 'possible worlds'. 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, but
he never said much about the nature of those propositions. (06)
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. (07)
So Kripke's semantics is a *proper subset* of Dunn's semantics.
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. (08)
PH> The laws and facts are stated explicitly as sentences in
> theories using Kripke-style semantics. (09)
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. (010)
PH> Check out any of the hundreds of papers on planning using
> a situation-calculus style of representation. (011)
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. To say anything about anything in a world, you need
to relate facts and laws (i.e., ontologies) about that world.
And that is where you need Dunn's semantics. But since the
people who wrote those papers never heard of Dunn's semantics,
they reinvented a very simplified special case. (012)
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. (013)
Please look at those papers: (014)
http://www.jfsowa.com/pubs/worlds.pdf (015)
http://www.jfsowa.com/pubs/laws.htm (016)
John (017)
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