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

 To: "[ontolog-forum] " Christopher Menzel Tue, 30 Mar 2010 12:30:41 -0500 <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) _________________________________________________________________ Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/ Config Subscr: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/ Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx Shared Files: http://ontolog.cim3.net/file/ Community Wiki: http://ontolog.cim3.net/wiki/ To join: http://ontolog.cim3.net/cgi-bin/wiki.pl?WikiHomePage#nid1J To Post: mailto:ontolog-forum@xxxxxxxxxxxxxxxx    (04) ```
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