Microtheories: genlMt vs. genls

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.

Proposition
/    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

Proposition*
/    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;