Re: builtins operating on rif:iri

Sandro Hawke wrote:
> ...
>>> ... and since it's not the same in every interpretation, it's not
>>> entailed.   I think I'm getting that.  So...
>>>
>>> positive-entailment
>>> PREMISE:    (empty)
>>> CONCLUSION: member(eg:foo, list(eg:foo eg:bar))
>>>
>>> negative-entailment
>>> PREMISE:    (empty)
>>> CONCLUSION: member(eg:baz, list(eg:foo eg:bar))
>>>
>>> positive-entailment
>>> PREMISE:    eg:baz = eg:bar
>>> CONCLUSION: member(eg:baz, list(eg:foo eg:bar))
>>>
>>> Agreed?
>> agreed.
> ...
>>> positive-entailment
>>> PREMISE:    eg:bar = 1
>>>             eg:foo = 2
>>> CONCLUSION: index-of(list(eg:foo eg:bar), eg:foo) = list(1)
>> yes
>>
>>> positive-entailment
>>> PREMISE:    eg:bar = eg:foo
>>> CONCLUSION: index-of(list(eg:foo eg:bar), eg:foo) = list(1 1)
>> Did you mean List(1 2)?
> 
> Yes, sorry.  (And I suspect we really want 0-indexed lists, but I'll
> stick with 1-indexed lists for this conversation, since I accidentally
> started that way.)
> 
>>> But what if the premise is empty?  I'm thinking that none of these
>>> entailments would hold...  (so these would be valid tests)....
>>>
>>> negative-entailment
>>> PREMISE:    
>>> CONCLUSION: index-of(list(eg:foo eg:bar), eg:foo) = list(1 1)
>> Yes
>>
>>> negative-entailment
>>> PREMISE:    
>>> CONCLUSION: index-of(list(eg:foo eg:bar), eg:foo) = list(1)
>> No. eg:foo is mapped to the same object in every interpretation. Let's
>> call this object a. And let's say eg:foo is mapped to b. Then
>> list(eg:foo eg:bar) represents the sequence (a,b). And certainly the
>> object a appears in the first position of this sequence.
>>
>> So, this should be a positive entailment test.
> 
> Well, I'd agree that in all interpretations, there's a match in the
> first position.  But in some interpretations there's also a match in the
> second postion (namely interpretations where eg:foo=eg:bar).  So, in
> some interpretations, the left side of the equals is interpretated as
> list(1) and in others it's list(1 2).  So, I think that means the
> equality doesn't hold in all interpretations, and the proposed
> conclusion is not entailed...

You are right. My mistake.


Best, Jos

> 
> Right?
> 
>      -- Sandro

-- 
+43 1 58801 18470        debruijn@inf.unibz.it

Jos de Bruijn,        http://www.debruijn.net/
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