RE: SWRL (FOL) n-ary relations

From: Wagner, G.R. (
Date: 12/14/04

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    [original qestion by MD]    Can we come
    up with an n-ary representation that's significant simpler or
    otherwise better than the unary/binary SWRL representation?
    [GW]    What do you mean with "significant simpler or otherwise better"?
    The issue here is simply that "objectifying" a relation may be
    unnatural and create some undesirable (and unnecessary) overhead
    in the language.
    [PH]    What kind of overhead? Why would this create any overhead?
    [GW]    If you don't see the overhead, this simply shows that you don't 
    have much experience with coding practical appplications. Or you may 
    be in the position of an assembler programmer who doesn't want to see 
    the unnatural overhead of coding a while loop with a jump/goto
    [GW]    In foundational ontology, one makes a distinction between formal
    and material relations (both of which would be represented with the help 
    of predicates).
    [PH]    ?Does one, indeed? That seems to depend a lot of which one one 
    happens to be. Is there any philosophical, mathematical or practical reason 
    for making such a distinction? 
    [GW]    Roughly, this distinction corresponds to the practical distinction 
    between predefined and user-defined properties/functions/relations in
    computational formalisms. So, yes there is a practical reason for making 
    this conceptual distinction. A philosophical reason for it may be the 
    desire to explain why some relations (such as those used in mathematics)
    have an extensional semantics and others have an intensional semantics. 
    What methodology or basic theory is used 
    to justify making distinctions like this? And what does this particular 
    distinction even mean?
        [Later.  I have now read some papers on the subject. The definition 
    appears to be purely circular: a relation is 'formal' if it is an extension which 
    applies directly, and is 'material' if it is an individual with a relational extension. 
    End of story. 
    [GW]    It's not quite that simple, unfortunately. Most people have some intuitive 
    understanding of what is a formal relation because they know orderings and 
    other relations from mathematics. An attempt to characterize the difference between 
    those formal relations and other relations (between individuals that have a "history")
    is to point out that (instances of) these material relations hold between their relata 
    because there is an individual (such as an event or a process) that affects the
    history of (and that existentially depends on) these relata. This is the case for 
    relations such as "Person buys Product from Vendor" or "Person kisses Person", 
    while it is not the case for relations such as "Point1 is between Point2 and Point3"
    or "Person is taller than Person" (the latter is a relation between the individual 
    heights of two persons, being qualities in the underlying "conceptual space"
    according to the theory of Peter Gärdenfors presented in his book "Conceptual 
    Spaces: the Geometry of Thought", 2000).
    ...; and the elaborate but misguided ideas emerging from the Leipzig institute do 
    not stand up to even a moment's close analysis; ...
    [GW]   Note that there are two "Leipzig institutes" (that have arised from a schism)
    and that I was referring to the work of Heinrich Herre and others on what they
    call "General Formal Ontology (GFO)" and "General Ontological Language (GOL)".
    Please don't confuse this with "BFO" as proposed by others and Smith, whose
    work is less profound. 
    What would be the basis for rejecting a claim that *any* relation defines a relator universal? 
    [GW]    A relator universal is an intensional concept, while formal/mathematical relations 
    are extensional. 
    ... you have no right to prevent me treating your 'formal' relations 
    as 'material' relations: unless, that is, you want to claim that this is a *logical* distinction. 
    [GW]    No, of course, the distinction between formal and material relations is not a 
    logical one. Most of the conceptual distinctions we make in order to understand the
    real world and to construct working computational systems are not logical! 

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