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Re: [ontolog-forum] Ontology and Databases

To: "[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Christopher Menzel <cmenzel@xxxxxxxx>
Date: Sat, 28 Oct 2006 13:20:41 -0500
Message-id: <184A3FFC-0A42-44AD-9D1E-C64208FABF52@xxxxxxxx>
> I've been away for a week at an ISO meeting working on ISO 15926,
> so I've found it difficult to keep up with things here, so unless
> its my imagination I think we had an exchange after your note
> below when you said that the data models in CL were really data
> models of the syntax, not of the underlying logic (or that's how
> I understood you).
> That is a shame,    (01)

Er, a shame?  Well-defined logical languages are universally  
presented by stipulating a basic lexicon (or at least a set of basic  
lexical categories), a recursive grammar that defines the well-formed  
expressions of the language in terms of the basic lexicon (which can  
be also be presented in the form of a data model), and a formal,  
mathematical semantics, or model theory, that, first, interprets the  
elements of the basic lexicon and then recursively defines how the  
complex expressions generated by the grammar are to be interpreted as  
a function of their component parts.  This is pretty much how CL  
defines its various dialects.    (02)

> because I do have some questions that I consider to be ontological  
> questions about CL (or pretty much any other
> logic). Perhaps you can help?
> What is a variable?    (03)

Well, most elementary logic texts take variables simply to constitute  
a basic lexical class.  Semantically, (first-order) variables are  
typically assigned some element of the universe of an  
interpretation.  CL, I should note, does not have a separate lexical  
category for variables.  It only has what are called "names" that can  
play any of the four traditional logical roles of variable,  
individual constant, function symbol, and relation symbol.    (04)

> What is a free variable?    (05)

A variable is free in a formula if some occurrence of that variable  
in the formula is not in the scope of a quantifier for that variable.    (06)

> What is a universal variable?    (07)

Well, that's not standard terminology, so I can't be sure what you  
have in mind.  A universally quantified variable occurrence is  
(roughly) one that falls within the scope of a universal quantifier.   
(That's not quite right, but it's close enough.)    (08)

> What is an existential variable?    (09)

Change "universal(ly)" to "existential(ly)" in previous sentence.    (010)

> What is a proposition?    (011)

That is an extremely fluid term.  "Proposition" sometimes just means  
"sentence".  If you mean something nonlinguistic, then there are  
numerous roles that philosophers, linguists, and logicians have taken  
propositions to play, notably, the can serve as the meanings of  
declarative sentences and as the objects of intentional attitudes  
like belief.  I recommend Matthew McGrath's article on propositions  
in the Stanford Encyclopedia of Philosophy for an excellent  
overview.  There are no propositions in a nonlinguistic sentence in  
CL, though the IKL extension of CL does contain a robust theory of  
propositions.    (012)

> What is an assertion?    (013)

Another fluid term.  Depends on the theory.    (014)

-chris    (015)

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