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Re: [ontolog-forum] Re Foundation ontology, CYC, and Mapping

To: "[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Christopher Menzel <cmenzel@xxxxxxxx>
Date: Tue, 30 Mar 2010 12:30:41 -0500
Message-id: <305EF9D1-C553-48C4-97F3-7BCB8D6D39D1@xxxxxxxx>
On Mar 29, 2010, at 10:46 PM, John F. Sowa wrote:
> ...
> KDK> Combinatory logic, by the way, is even "simpler" than FOL:
>> the whole thing can be defined with only two operators, named
>> "S" and "K".  And you can define FOL in combinatory logic.
>> So why don't we adopt that as the one, true uber-standard?
>> What could be simpler?
> Combinatory logic is just a different syntax for FOL.  It could be
> defined as a dialect of Common Logic, if anyone wanted to do so.    (01)

Whoa, combinatory logic is way stronger than ordinary FOL.  (I suspect you have 
in mind syntactically (and historically) related systems like the predicate 
functor calculi of Quine and Schönfinkel that do away with the apparatus of 
quantifiers and variables.)  Combinatory logic is expressive enough to 
formalize recursive function theory and, hence, exhibits Gödel-style 
incompleteness.  Its power aside, it would be a terrible choice as an 
"über-standard" for knowledge engineering.  Number of primitives is no measure 
of simplicity.  Combinatory logic is intuitively very difficult to grasp and 
use -- its basic ontology consists of functions rather than objects, properties 
and relations and, concomitantly, its syntax is based on function application 
as opposed to FOL's predication, which arises naturally out of the Noun Phrase 
/ Verb Phrase structure of ordinary language -- perhaps the central reason why 
it is so easy to learn.  A more meaningful measure of the intuitive difficulty 
of combinatory logic is seen in the fact that, although it traces its origins 
to at least the 1920s (with even deeper roots in the 19th century), it didn't 
have a model theory until Scott's (very beautiful, but very complex) fixed 
point construction in (IIRC) the early 1960s.    (02)

Chris Menzel    (03)

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