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Re: RDF Concepts and Abstract Data Model: semantics

From: pat hayes <phayes@ai.uwf.edu>
Date: Thu, 5 Sep 2002 20:20:40 -0700
Message-Id: <p05111b03b99dca7739af@[65.212.118.251]>
To: Jerome.Euzenat@inrialpes.fr (Jerome Euzenat)
Cc: www-rdf-comments@w3.org

>Hi,

Hi Jerome

Parts of the wording about model theory that you object to originate 
with me, so I will take it upon myself to respond.

>	about the "Resource Description Framework (RDF):Concepts and 
>Abstract Data Model" document, I have comments about one minor part 
>(viz. 2.3.1 Formal semantics):
>
>| To serve this purpose, certain meanings of RDF statements must
>| be defined in a very precise manner
>
>why "certain" and which ones?

Good question. Most of them, but not all: there are some constructs 
in RDF which cannot be given a coherent model theory (without 
enormous effort), but nevertheless are already in widespread use, so 
are being preserved in order to not interfere with 'legacy' code. 
These include the reification constructs, for example. (I know that 
one *could* give an MT for reification fairly easily, but that 
meaning would not in fact coincide with the legacy uses, which are 
more to do with tagging than true meta-description.)

>
>>Model-theoretic semantics assumes that a language refers to a 
>>'world', and describes the minimal conditions that such world must 
>>satisfy in order to assign an appropriate meaning for every 
>>expression in the language.
>
>"a language refers to a 'world'" is at least misleading:
>- this is rather the assertions in the language which refer to the world.
>- the word "a" here could lead the reader to equate one language or 
>one set of assertion to one world, though the purpose of model 
>theory is not to tie the assertion to one world but rather to 
>consider all the possible worlds.
>
>I offer the replacement:
>"Model-theoric semantics defines the meaning of expressions in the 
>language through a mapping (called interpretation) from a language 
>to worlds. A set of assertions in the language, thus induce 
>constraints on the acceptable interpretation (called model) of these 
>assertions. The meaning of an expression is defined with regard to 
>its interpretation in all the models."
>
>I am sure that this is too technical,

Right, it is. I gave a presentation to the WG based on this classical 
way of talking about interpretations, and it went down like a lead 
balloon.  There are many ideas involved in model theory, and most 
readers will not be familiar with most of them. Try reading the above 
sentence as a very first preliminary introductory sentence to get 
across one of the basic ideas.

But I take your point about the potentially misleading connotation of 
the use of "a" and will strive for a better phrasing.

>  maybe reducing this part and refering to RDF-MT document is an 
>easier alternative.
>
>>  A particular world is called an interpretation, so that model 
>>theory might be better called 'interpretation theory'.
>
>Not accurate: an interpretation is a mapping from the language to 
>the world. Indeed there can be many interpretations mapping to the 
>same world.

That depends on what you count as a 'world'. I thought of trying to 
draw careful distinctions between an interpretation mapping and an 
interpretation structure, but the problem is to get the ideas across 
to a casual reader before their eyes glaze over. It seemed simpler to 
simply treat each interpretation (that is, a structure plus an 
interpretation mapping into the structure) as a single entity and 
call it a 'world'.  That latter term has no precise mathematical 
meaning in any case.

>
>A model of a set of assertions is an interpretation that satifies 
>all the assertions in the set (i.e., which maps it to the element of 
>a distinguished subset of the world for being very general, very 
>often the set { true }). So model theory is well named.

Yes, I know that is what 'model' means in model theory, but 
throughout the rest of the English-speaking world it means almost the 
exact opposite: that is, a 'model' is usually taken to be something 
(often something inside the computer) which is simpler than a 'world' 
and is used to model it, not as meaning the world which is modelled 
by the description. The very term 'data model' in the title of the 
document uses it in this way, for example. This unfortunate mismatch 
between the use of 'model' in mathematical logic and its use 
throughout most of computer science (and in fact science and 
engineering  more generally) regularly leads to tangles of confusion, 
which is why I deliberately avoided the use of the word in the RDF MT 
documentation, and referred instead to 'satisfying interpretations'. 
More long-winded but far less confusing.  The next version of the RDF 
MT document will not even use 'model theory' in its title.

>
>Also in 3.5 RDF graph, in the Note:
>- RDF Graphs are "node-labeled, edge-labeled directed multi-graphs" 
>(with no disjointness constraints between node-labels and 
>edge-labels): the multi- aspect is not in the note (i.e., that there 
>can be several arcs between the two same nodes -- maybe with 
>different labels).
>
>Just for being nitty-gritty,

Right, getting the graph terminology straight has been a hassle. I 
myself now prefer to simply define it as a set of triples, and 
relegate the graph terminology to the realm of graphics.

Pat Hayes
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Received on Friday, 6 September 2002 04:55:35 GMT

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