Re: canonical ordering (Re: Converses?)

Jim Fulton <>
Date: Thu, 28 Mar 1996 08:19:45 -0800
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To:,,, (Bill Brayman),
From: Jim Fulton <>
Subject: Re: canonical ordering (Re: Converses?)
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At 02:31 PM 3/27/96 -0800, Bill Brayman wrote:
>in ordinary language we often mark sentence components to indicate the role
the element is playing such as(using Pat's example):
>So, to suggest a line of reasoning for Pat's question, his relation
C(x,y,z,u) really is a constellation of relations that serve to define
argument position.  Then, a KR language must have a way to express the
composite. I know this can be flattened into raw FOL syntax.  But, I believe
there is some kind of inferencing shortcut involved when using "roles" to
define argument positions related to the original issue of developing
hierarchies on relations.  By the way, I don't mean to introduce foreign
terminology, this is essentially the bipartite graphing approach (links
between boxes and circles) of conceptual graphs.
In constructing the Semantic Unification Meta-Model (SUMM) for STEP a few
years ago, we formalized this feature of natural language by requiring
explicit "role-indicators" such as Bill suggests.

The reason for this was our need to "semantically unify" predicates from
languages that ordered their predicates differently or even had different
arities or roles for predicates.  For example, the Boeing database
equivalent of the sentence "airplane xyz was bought by United Airlines" is
semantically equivalent to the United Airlines database equivalent of the
sentence "airplane xyz was bought from Boeing", and both are semantically
equivalent to "Boeing sold airplane xyz to United Airlines" which might
appear in the FAA database, and to "United Airlines bought airplane xyz from
Boeing" which might appear in the IRS database.  By making the roles
explicit in the canonical SUMM representation, we could map any of these
partial or reordered representations to the common one.  

The formal semantics for the SUMM also "justified" the inference from
"United Airlines bought airplane xyz from Boeing" to "airplane xyz was
bought from Boeing", without the brute force assertion that "airplane xyz
was bought from Boeing" was elliptical for "airplane xyz was bought by
someone from Boeing".  Without going into the details, the technique
exploited the fact that when role-indicators are explicit,

(a) arity need not be fixed,
(b) order is irrelevant,
(c) roles can be truly optional,
(d) roles can be repeated in the same elementary sentence.

A further corollary of (d) is that symmetric predicates can often (normally)
be treated as predicates in which both participants play the same role.  For
example, "John married Betty" and "Betty married John" are treated in
classical formal semantics as two different sentences.  To be true the pairs
<John, Betty> and <Betty, John> must be in the extension of "married".
There is presumably an axiom of symmetry which assures that the sentences
are equivalent, but the formal semantics does not provide any explanation of
this axiom.  The canonical representation in the SUMM, however, is
"married((subject, John), (subject, Betty))", which is syntactically similar
to "John and Betty were married".  This sentence is true when the set (not
the ordered set) {<*subject, *John>, <*subject, *Betty>} is a member of the
extension of "married".  More precisely, that  sentence is true when that
set is a SUBSET of a member of that extension).  Indeed, "John and Betty
were married", "John married Betty" and "Betty married John" are all made
true by the more complex {<*subject, *John>, <*subject, *Betty>, <*by,
*Parson Brown>}.  Thus the SUMM formal semantics provides a formal
justification of the inference from "John and Betty were married by Parson
Brown" to "John married Betty".

Furthermore, since all of these different sentences can now be interpreted
as different (and possibly partial) representations of the same "object" in
the extension of the  predicate, it begins to look like that "object" can be
interpreted as a state of affairs, whose inclusion in the extension of the
predicate not only renders a class of sentences true, but might also itself
stand in relationships to other states of affairs.

In other words once we sever the formal meaning of a sentence from the order
of its presentation, there are some interesting philosophical questions that
might benefit from formal analysis.


* The above remarks do not necessarily reflect the position of               *
* The Boeing Company or any of its employees (including me).                 *
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