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Re: [ontolog-forum] What is the role of an upper level ontology?

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From: Tara Athan <taraathan@xxxxxxxxx>
Date: Thu, 16 May 2013 12:14:34 -0400
Message-id: <519505EA.8080006@xxxxxxxxxx>
I would like to clarify on some remarks recently made about Common Logic.    (01)

On 5/14/13 12:00 PM, John F Sowa wrote:
>    5. Common Logic has only one domain of quantification,
* A CL interpretation does indeed have one domain of quantification 
(called the universe or domain of discourse). The interpretation of a 
particular CL text may require the consideration of more than one domain 
of quantification , due to portions ("modules" in the current version) 
being required to satisfy interpretations created by restricting 
(shrinking) the domain of quantification.  This has been shown to be 
syntactic sugar - it is always possible to simply add a condition to the 
quantification in order to restrict it to a certain subset of the domain 
of quantification.    (02)

In addition a CL interpretation allows for reference to entities that 
are outside of the domain of quantification. This larger set of entities 
is called the universe of reference.    (03)

> and the
>       CL syntax allows any entity to be used as a function or
>       relation with any number of arguments.
* A Cl interpretation associates a name with one entity in the domain of 
reference. Each CL interpretation also associates one function and one 
relation with every entity in the domain of reference. The same name is 
used to indicate the application of this function or relation, 
distinguished by the syntactic context in which the name appears. This 
is not, in my view, the same as the entity being "used" as a function or 
relation - that suggests that the entity has some intrinsic functional 
or relational characteristics, when in fact the association of an entity 
with a function or relation is created by the interpretation. A 
different interpretation could associate a different function or 
relation with the same entity.    (04)

>   In that sense,
>       one could say that CL has an implicit one-category ontology.
I would say that CL has an implicit five-category ontology. There are 
the three categories of entity, function and relation. The category of 
entity is further divided into the domain of discourse and the 
complement of the domain of discourse within the universe of reference.    (05)

The functions and relations can also be partitioned into discourse and 
non-discourse. While it is possible to have the same function/relation 
associated with a discourse entity and also with a non-discourse entity, 
any function/relation associated with some entity in the domain of 
discourse could be considered a discourse function/relation, due to it 
being "reachable" by a quantification such as    (06)

(exists (x)  (= x(a) b) )    (07)

This gives six categories ( discourse and nondiscourse relations, 
functions and entities). However the last of these (nondiscourse 
entities) is irrelevant from a practical standpoint, as a text that 
refers to a nondiscourse entity  (in an equation, or as a function or 
predicate argument) should[1] never be satisfiable.    (08)

CL does not impose any explicit ontology on entities. It is up to the 
author whether to include axioms that require a particular entity or 
group of entities to be the same as the function or relation associated 
with them.    (09)

[1] The published CL standard has some holes in it so that this 
obligation is not adequately met. The upcoming revision of the CL 
standard (http://ontolog.cim3.net/cgi-bin/wiki.pl?CommonLogic_V2) will 
address this issue.    (010)

Tara    (011)

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