Date: Fri, 9 Sep 94 11:31:06 PDT
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To: (Fritz Lehmann)
From: (Anthony K. Sarris)
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Just to avoid any misconceptions when you say:

>Ideally, an
>international standard for logic should be based on some expertise
>rather than guessing.  Meanwhile, we need a standard soon, so let's
>adopt one with the option of using either First-Order semantics or
>higher-order semantics.  As a potential implementer of common-sense
>ontologies for practical use, I may not want the First-Order
>peculiarities imposed on me.  Give me a choice, within the standard.

Let me make clear that neither ANSI X3T2 nor ISO/IEC/JTC1/SC21/WG3 CSMF RG
is intending to develop an international standard for logic. The problem we
ran into was that we wanted to use symbolic logic (of some form) as a means
of expressing and manipulating semantic constructs useful for conceptual
modeling (i.e., for producing conceptual schemas in the ISO TR9007 sense).
There was no single source (ISO standard or otherwise) that we could drawn
upon as the definitive source for logic. So we decided to specify within
the Conceptual Schema Modeling Facility standard (which is the actual
standard we are working on) the logic formalism that we felt was needed to
support our purposes. That formalism almost certainly won't deal with all
of logic, but only those aspects we view as necessary for what we want to
do with a CSMF. Also, what John Sowa and others involved directly with CGs
decide to do with CGs in general is largely independent of the ANSI X3T2
effort and X3H4 IRDS effort (which is now combined with the X3T2 effort
anyway). Again, we will drawn upon appropriate aspects of CGs, KIF, SUMM
and whatever else to form a suitable basis for supporting the CSMF
standards work.

For that work, it does seem fair to ask and answer the question of whether
first order logic formalisms (including n-order logics derived from them)
are sufficient to support conceptual modeling, or whether an explicitly
higher-order formalism should be used, or both. You say:

>The syntax and semantics of Conceptual
>Graphs or of KIF would be the same, but the CSMF would have provision
>for a "semantics switch" for those who prefer not to live with the
>First-Order limitations embraced by Mike Genesereth and John Sowa.

I'm not sure how this 'switch' would work in practice and how that would
affect the specification of the CSMF standard, but it is something to
consider. Like others in X3T2, I'd like to study your list of things for
which higher-order logic seems to be needed, as well as counter-arguments
that most if not all of those things can be accomplished with higher-order
formalisms derived from FOL.

As far as I'm concerned, the most important aspect of higher-order logic is
support for context and other forms of modalization. That includes
quantification and qualification over relations, functions, etc. rather
than just individuals, and therefore necessitates some means of handling
higher-order logic. Sowa allows this in CGs through nesting of graphs. I
don't know how or if KIF allows this: maybe someone can provide this
information. Chris Menzel suggested that there also other approaches within
the FOL school to allowing this sort of thing, in particular quantifying
[individuals] in particular tuple positions, as well as only specific
relations or properties involving an individual. Additional details and an
example here would be helpful to better understand how this works.

Internationally, there may well be objections to utilizing anything outside
traditional FOL, as some national bodies have already expressed concerned
that higher-order logics are simply too vaguely defined -- i.e., that they
are largely the subject of research not general practice -- and are
therefore not appropriate for inclusion or application within an ISO

Having said all that, I think this discussion is quite useful, and as a
X3T2 member I appreciate such useful information from people who couldn't
otherwise regularly participate in the on-going standards work.

Tony Sarris

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