I agree with almost everything you said, but have some questions
about inverting the n-ary to binary relation mappings: (02)
1) If one has an incomplete (partial) set of binary relation instances,
and one wants to reconstruct the n-ary relation instabce (e.g., to store the
binary relationships in an n-ary relation in a relational DBMS) what
does one do about the missing binary relation instances? Does one represent
the corresponding n-ary relation with nulls in the missing attribute
2) More generally, I am looking for literature (and perhaps software)
on translating queries against the binary relation model back into
queries of the n-ary relational model or into mixtures of the two.
Specifically, I am concerned about rewriting SPARQL queries
into SQL queries on into mixtures of SPARQL and SQL (i.e., some
relations are stored as binary relations in RDF and some as n-ary
relations in a relational DBMS). Any pointers
would be appreciated .... (04)
This problem arises in attempting to construct RDF/Owl/SPARQL
based systems which must co-exist with existing relational DBMS
Pat Hayes wrote:
> On Feb 10, 2009, at 4:45 PM, Mitch Harris wrote:
>> PH, JS, et al.:
>>> Semantically, 'give' has three participants. One or two may be
>>> omitted in a grammatical English sentence if they are obvious
>>> from the context. But they exist, whether or not the speaker
>>> or listener knows who or what they are.
>> To get back to a single relation that is stipulated rather than
>> follow the
>> many (interesting) lexical/semantic paths surrounding donation, let's
>> with 'give' having all three parameters.
> Which begs the question. But let us proceed.
>> Let me make what I think is the appropriate summary (yes many of the
>> following are arguable, and have already been argued, but there it is):
>> Given the ternary relation "Gives(A, B, C)" (which happens to mean
>> that A
>> gave B to C) we can easily encode it as three binary relations: assign a
>> unique x, then Gives1(x, A), Gives2(x, B), Gives3(x, C) is derivable from
>> the ternary relation and one can reverse the derivation.
> Not quite. There is no 'assignment' and no requirement of uniqueness.
> The translation into case/role binary form simply refers to the
> /existence/ of the giving action. Also, the translation is usually
> stipulated so that the original ternary (or whatever) relation becomes
> a predication establishing the event as having the appropriate verbal
> type, in this case a giving. So one gets the pattern:
> Foo(A, B, C)
> (exists (x)( Foo(x) & FirsCaseName(x, A) & SecondCaseName(x, B) &
> ThirdCaseName(x, C) )
> where the appropriate case/role names depend on the particuiar verb,
> but often have 'agent' as the first one.
>> Converting everything to binary has its benefits: homogeneous
>> representation, most concepts are already binary (except maybe database
> The most important advantages are (1) the case/role names identify the
> various arguments by name, making it easier to remember them (2) the
> second form allows partial information to be recorded and used
> naturally, and allows for arbitrary extensions, and (3) it also puts
> the actual event described by the verb phrase into the universe of
> discourse, allowing other properties and relations to be asserted
> about it. Finally (4) it means that a relatively simple notation
> (such as RDF graph syntax, ie a labelled directed graph) can be used
> to represent what seem on the surface to be much more complicated
> facts. This is probably the origin of the idea that 'most' relations
> are binary, which is actually much less obvious.
>> However, despite its simplicity, this equivalence/derivation is not well
> It is very well known in AI/KR, ontology engineering, formal logic and
> linguistics. Several widely used rule languages are based on it.
>> , and even when known it is counterintuitive to use (as humans usually
>> write these things).
> On the contrary, for rendering the meanings of simple English action
> sentences, it is actually in many ways more intuitive; and it supports
> important 'obvious' entailments. For example, if John gave a book to
> Mary, then it follows that Mary was given a book by John.
>> Could the n-ary/binary debate be settled by allowing binary to be the
>> machine language and n-ary be the higher level human written language?
> That is one way to proceed, but it ignores the intuitive and
> human-engineering advantages of the case/role form, such as its being
> easier to remember.
> This whole topic is a storm in a teacup. Real ontology engineering can
> all be done within binary languages such as RDF: this has been known
> for decades. For some purposes, allowing higher adicity relationships
> is advantageous, but even when they are possible, the classical
> case/role system is still widely useful. It is easy, if a little
> tiresome, to mentally translate back and forth between various surface
> conventions where needed, and also to write preprocessors which
> present any logical form in almost any way that a user feels
> comfortable with. Let everyone use their favorite notation, and we can
> easily translate between them when necessary.
> Pat H
>> Mitchell A. Harris
>> Research Faculty (Instructor in Computer Science)
>> Department of Radiology
>> Massachusetts General Hospital/Harvard Medical School
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