# [closed] Re: RDF Semantics: subinterpretations

From: Brian McBride <bwm@hplb.hpl.hp.com>
Date: Tue, 25 Feb 2003 14:37:57 +0000
Message-Id: <5.1.0.14.0.20030225143749.036fa8b8@localhost>
To: pat hayes <phayes@ai.uwf.edu>, herman.ter.horst@philips.com

```
At 14:33 24/02/2003 -0600, pat hayes wrote:

>>RDF Semantics document,
>>last call version, 23 january 2003
>>This comment was mailed earlier to the WebOnt WG [1].
>
>For the record, the editor accepts this as an editorial comment.
>
>>The definition of subinterpretation I << J in Appendix B
>>is not clear, as
>>it is not clear what a "projection mapping from IR into JR,
>>IS into JS, IL into JL and IEXT into JEXT" is.
>>IR and JR are sets, so the first part is clear: a function
>>from IR into JR. However, IS and JS are functions.
>>(What is meant by a mapping from a function to a function?)
>
>The concept is a familiar one in mathematics: it is often referred to as a
>morphism between functional categories.
>
>But the wording of the proofs of lemmas will be clarified and this
>
>>It seems that the following definition suits the intended
>>use in the Herbrand lemma:
>>
>>I is a subinterpretation of J, I << J, when there is a projection
>>mapping f : IR -> JR such that the following hold:
>>- f(IP) subsetof JP  [this is needed for the last condition]
>>- for each v in V, JS(v)=f(IS(v))
>>- for each typed literal l, JL(l)=f(IL(l))
>>- for each p in IP,
>>{ <f(x),f(y)> : <x,y> in IEXT((I(p)) } subsetof JEXT(f(p))
>>
>>Then, automatically, the property that is desired in the text
>>follows: any triple is true in J if it is true in I.
>
>Yes, quite, that is the intent of the current phrasing, stated in a
>lengthier form.
>
>There is an editorial issue generally in writing such things as this
>appendix. In many people's view, a document like this should not even have
>things like lemmas and proofs in it *anywhere*. To anyone trained in
>formal logic these results and the proof techniques are all elementary in
>any case. On balance, therefore, it seemed appropriate to give an
>expository outline of the basic proof techniques as an informative guide
>for some readers as well as providing others (such as yourself, Herman)
>with the opportunity to check the reasoning. However, to write out these
>proofs too formally and in too much detail does not seem appropriate, as
>this would make them unreadable by the novice and boring to the initiated.
>
>I will try to make the wording clearer, however, in the light of your
>
>Pat
>--
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```
Received on Tuesday, 25 February 2003 09:36:55 GMT

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