Re: Review of FLD

Michael Kifer wrote:
>>>> 2.4 Terms
>>>>
>>>> "Positional terms in RIF-FLD generalize the regular notion of a term used in 
>>>> first-order logic. For instance, the above definition allows variables 
>>>> everywhere, as in ?X(?Y ?Z(?V "12"^^xs:integer)), where ?X, ?Y, ?Z, and ?V
>>>> are > variables. Even ?X("abc"^^xs:string ?W)(?Y ?Z(?V "33"^^xs:integer)) is
>>>> a positional term (as in HiLog [CKW93]). "
>>>>
>>>> This idea goes back at least as far as Enderton, 1972, and has been used in 
>>>> implemented systems such as SNePS and Conceptual Graphs in the 80s.  Since 
>>>> Enderton published in '72 what was already a "well known encoding" of
>>>> predicate variables in FOL, I don't think it's accurate to say this
>>>> "generalizes...FOL". 
>>>> The fact is that this IS perfectly first-order.
>>> The idea goes back to Henkin. However, take another look at these terms and you
>>> will see that some are not expressible in Henkin's syntax or in Common Logic.
>>> It is in this context that HiLog is referred to. Second-order variables by
>>> themselves are not worth bothering to reference, as this is common knowledge.
>> Yes of course, but this example is of positional terms and is completely first 
>> order.  What about it do you consider non-Henkin (other than the datatypes), or 
>> non-CL?  Again, I'm just talking about the positional terms item, not FLD terms 
>> in general.
> 
> Is ?X("abc"^^xs:string ?W)(?Y ?Z(?V "33"^^xs:integer)) an instance of Henkin's
> or CL syntax? Hint: check what plays the role of a function here.

Ah, I see.  Henkin did not have functions.  Yes, this is valid CL syntax, and is 
still compact so still first order.  My understanding of compactness is that 
functions and constants are interchangeable in terms of their impact on it.

-Chris

-- 
Dr. Christopher A. Welty                    IBM Watson Research Center
+1.914.784.7055                             19 Skyline Dr.
cawelty@gmail.com                           Hawthorne, NY 10532
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Received on Tuesday, 19 May 2009 13:12:11 UTC