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Microtheories: genlMt vs. genls

From: Richard H. McCullough <rhm@cdepot.net>
Date: Wed, 3 Sep 2003 23:40:17 -0700
Message-ID: <000b01c372b1$e481de40$bd7ba8c0@rhm8200>
To: "www-rdf-interest at W3C" <www-rdf-interest@w3.org>
Cc: "Guha, R. V." <guha@guha.com>, "Reed, Stephen L." <reed@cyc.com>, "McCool, Rob" <robm@stanford.edu>, "KR-language" <KR-language@YahooGroups.com>
These notes clarify an issue that has confused me.
I hope you can benefit from my experience, and
avoid confusion.

Recall that a Microtheory is a collection of propositions.
If we consider subclasses of propositions, we obtain a
genls hierarchy of propositions, e.g.

/    BroadMicrotheory
//        BaseKB
//        UniversalVocabularyMt
/    FictionalContext
/    GeneralMicrotheory
//        AgentGMt
//        BaseKB
//        NaivePhysicsMt
//        PeopleMt
/    VocabularyMicrotheory
//        UniversalVocabularyMt

defined by the relations

BroadMicrotheory genls Proposition
BaseKB genls BroadMicrotheory, GeneralMicrotheory

If we consider the closure Mt*, obtained by adding
all the logical implications of the Mt propositions,
the hierarchy turns upside down:  The smaller the
microtheory, Mt, the larger the closure, Mt*.  The
above proposition hierarchy is mapped to

/    AgentGMt*
//        GeneralMicrotheory*
/    BaseKB*
//        BroadMicrotheory*
//        GeneralMicrotheory*
/    FictionalContext*
/    NaivePhysicsMt*
//        GeneralMicrotheory*
/    PeopleMt*
//        GeneralMicrotheory*
/    UniversalVocabularyMt*
//        BroadMicrotheory*
//        VocabularyMicrotheory*

and defined by the relations

Proposition* is Proposition
BaseKB* genls Proposition*
BroadMicrotheory* genls BaseKB*, UniversalVocabularyMt*

Now comes the confusing part: the above set
of relations is rewritten without the *s as

Proposition is Proposition
BaseKB genlMt Proposition
BroadMicrotheory genlMt BaseKB, UniversalVocabularyMt

To avoid confusion, remember the genls and the *.

Dick McCullough
knowledge := man do identify od existent done;
knowledge haspart proposition list;
Received on Thursday, 4 September 2003 02:58:26 UTC

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