Ramesh Patil <>
Message-id: <>
To: (David McAllester)
Subject: Re: KIF 
In-reply-to: Your message of Tue, 07 Jan 92 13:44:41 -0500.
Date: Tue, 07 Jan 92 10:57:44 PST
From: Ramesh Patil <>
    On the contrary, there is a growing interest in higher order logic,
    or at least a carefully chosen subset of higher order logic that
    will allow us to naturally represent many of the everyday sort of
    statements (and allow reasonable inferences from them).

David writes:
  Sounds interesting.  Have you considered whether the subsets of
  higher order logic allow truely increased expressive power?  For
  example, do they allow a definition of transitive closure?  The Kl-ONE
  primitives I am aware of do not really extend the expressive power
  beyond that of first order logic.  Why not simply allow
  arbitrary quantification over functions and predicates?

 What you say is true.  The place where KL-ONE like syntax goes
beyond the normal first order logic is when they deal with number
restrictions.  But that aside, the issue of transitive relations has
been around in KL-ONE community.  As a matter of fact NIKL syntax
allowed you to define transitive relations such as CONNECTED-TO by
clever use of compose relations etc.  But the classifier would choke
on the definition.  I think the primary reason why higher order
definitions such as transitive relations and more powerful
quantification is not present in KL-ONE languages is
because we have not figured out how to deal with them effectively.

PS: Loom allows you to define transitive closures of relations, as
new relation.  But this new relation is treated as "PRIMITIVE". 
Thus although the system can compute the relation over a KB, it does
not reason from its definition.

 - Ramesh