# Re: Higher-order KIF & Conceptual Graphs

Tomas Uribe <uribe@CS.Stanford.EDU>
```Reply-To: cg@cs.umn.edu
Date: Tue, 9 Nov 93 11:53:23 -0800
From: Tomas Uribe <uribe@CS.Stanford.EDU>
Message-id: <9311091953.AA10690@Xenon.Stanford.EDU>
To: interlingua@ISI.EDU
Subject: Re: Higher-order KIF & Conceptual Graphs
Cc: cg@cs.umn.edu
```
```Fritz Lehmann writes:

>> KIF and Conceptual Graphs now make no provision for
>> higher-order concepts with any semantics at all.  Gruber's
>> Ontolingua makes a stab at it, as do Boley's DRLHs.  We
>> need relations among relations, relations between
>> relations and their own arguments, functions of functions,
>> and so on, not just relations among individuals.  (For
>> some purposes one might conceivably want relations defined
>> on connectives, as in the works of Zellweger, Menger or
>> Stern.)

Um, Chapter 8 of the KIF reference manual describes how functions
and relations can be defined... Given these definitions, one can
proceed to quantify over them, and thus define functions of functions,
relations over relations, and so on (i.e., the "individuals" over
which the functions and relations range over are functions and
relations themselves).

Also, the "metalanguage" facilities described in Chapter 9 can
be used if one wants relations over connectives:
quotation can be used to define the syntax of the language
at hand, and predicates that take sentences as arguments can be
used to define semantics and/or proof theory...
Relations between functions and their arguments could be similarly
defined, provided one has a formal definition of what an "argument" is.

>> I think I've cited examples of about five or six
>> kinds of higher-order things that users might want to say
>> for practical applications, which are simply impossible to
>> say in current (First-Order) KIF or CGs.

Have these examples been sent out to the Interlingua list?
I don't recall seeing them...

Cheers,

- Tomas E. Uribe			uribe@CS.Stanford.EDU

```