RE: SWRL (FOL) n-ary relations

From: Christopher Welty (
Date: 01/18/05

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    Pat Hayes <> 
    01/18/2005 05:22 PM
    "Wagner, G.R." <>
    Christopher Welty/Watson/IBM@IBMUS, <>, "Mike Dean" 
    <>, <>, "Guizzardi, G. (Giancarlo)" 
    <>, <>
    RE: SWRL (FOL) n-ary relations
    [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.
    The phrase could be referring to extra complexity in the logical encoding, 
    or to computational overhead in any of various kinds of processing engine. 
    These are not the same, and in some cases may be opposed to one another. 
    In particular, a 'conceptual' overhead can in some cases yield a 
    computational improvement (the restrictions needed for DL conformance are 
    one example.) I would have liked to had the intended meaning clarified.
    I suspect what is meant by "overhead" here is simply that when relations 
    are "reified" you end up with more tuples.  As a simple example, if the 
    extension of the (ternary) relation ChangePos is {<a,b,c>} then the 
    standard kind of reification into binary relations would result in the 
    extension of the (unary) relation ChangePos' being {C1} and introducing 
    three binary relations, lets say Who, To, From whose extensions resp. are: 
    {<C1,a>} {<C1,b>} and {<C1,c>}
    So this style of relation reification which is typically used when there 
    is a limit to unary and binary predicates (I'm assuming that is what you 
    are talking about, I don't know how I got into this discussion)  results 
    in "overhead" of three tuples, where a system that allows higher arity 
    would have only 1 tuple.  Is that clear?
    To make the particular point more forcibly, Common Logic allows one to 
    write a relation name as an individual, and to quantify over names in 
    relation position: the model theory objectifies all named relations for 
    free, as it were. Now, what overhead do you see this as introducing?
    Indeed, this is a powerful facility, and would be extremely useful in 
    specifying interoperability between languages like RDF & OWL (that are 
    limited to binary relations and require some special handling for higher 
    arity relations such as the style of reification exemplified above) and 
    systems like relational DBs, KIF, etc.
    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
    I have been at various times at several different such positions. My 
    general conclusion is that terms like 'unnatural' have no fixed or 
    objective meaning, but simply indicate an implicit reference to some 
    unspoken background bias or cultural assumptions made by the author. It is 
    often useful to have these made explicit wherever possible. 
    [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 
    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.
    Wow. I really would like to see this analogy defended in a serious 
    publication.  For the present I will simply register my extreme cynicism 
    regarding any such analogy, and a rejection of the 'formal/material' 
    contrast. If this contrast really were basic or important, then formal 
    relational logics would be surely have needed to have reinvent it: but 
    they have not found any such need.
    There must have been parts of this exchange that were snipped before I was 
    included, because I don't see the connection at all between relation 
    reification and the formal/material "distinction".
    Anyway, this distinction, which is certainly debateable, is one which 
    claims some relations are somehow more "foundational", let's call it, than 
    others.  THe distinction is the same as the "formal" vs. "material" 
    ontology distinction.  I think Barry would try to define it, or maybe he 
    has published something that does, as relations that would exist even if 
    people weren't there to record them.  PartOf, for example, is often 
    considered a formal relation, whereas "SpouseOf" is not.
    However I would be quite surprised to hear anyone claim the point is not 
    debateable.  There is certainly nothing at all special about formal 
    relations that require special treatment in logic, from (my own) practical 
    perspective formal relations are simply those with the highest degree of 
    reusability across domains.
    So, yes there is a practical reason for making
    this conceptual distinction.
    There might be if that analogy made sense.
    A philosopher may claim that formal relations are the underlying threads 
    that sew the universe together, so to speak;  if you wanted to describe 
    the universe you would need nothing else.  Still, I don't see much 
    practical value in making the distinction other than being able to judge 
    which relations may be more reusable.
    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. 
    I do not know of any linguistic or philosophical justification for 
    claiming that some relations are intensional while others are extensional. 
    (Note, there are reasonable debates about whether relations should be 
    construed as intensional or extensional: but those refer to relations in 
    general. What I find implausible is the idea that both kinds are 
    I've never heard of this before either, it seems rather nonsensical. 
    Intensional vs. extensional semantics seem like a completely different 
    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 
    understanding of what is a formal relation because they know orderings and
    other relations from mathematics. 
    Perhaps I did not make myself sufficiently clear. I do not accept any 
    distinction between 'formal' relations and other kinds of relations (in 
    fact between any kinds of relation) . Your discussion seems to presuppose 
    this meaningless distinction.
    Well, I don't think your accepting it or not makes the idea go away.  But 
    the distinction certainly seems to me completely subjective.  In fact, I 
    can imagine building different theories (or logical descriptions) of the 
    universe using different sets of assumptions as to what is "formal" and 
    what is not.
     (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. 
    Again, I find this entire discussion to be profoundly confused. 
    Me, too.  Perhaps someone could clue me in as to the history and context.
    Of course there are material entities which have a history, and are 
    distinct from nonmaterial entities such as numbers. However, none of that 
    requires us to distinguish two kinds of relation. 
    On the contrary, it seems to me that makes four kinds of relations: 
    material x material, material x non-material, ...
    In fact, the contrary:if one makes the temporal structure and dependencies 
    explicit, as will in fact be required in any practical ontology, then all 
    relations become timeless. 
    HERETIC!!!!! Thou hast been revealed!!!  I am NOT A TEMPORAL PART!
    The resulting simplicity has been rediscovered many times: by McCarthy in 
    the situation calculus, by Kripke in his possible-world modal semantics 
    and the associated modal-to-FOL translation scheme, and by linguists 
    studying tense and case grammars. It ought by now to be part of the 
    standard stock-in-trade of any working ontologist. 
    I think I agree with that, actually, however it (theories of temporal 
    parts) should be a tool like anything else, not a religious conviction. 
    There appear to be times when it is useful, and times when it is a royal 
    pain.  Much like its advocates.
    It can be summed up in a slogan: if you think that you need more than one 
    kind of relation, look to the things that the relation holds between. Make 
    distinctions there, and classify kinds of thing rather than kinds of 
    Err...are you saying you cannot have more than one kind of relation 
    between the same kinds of things?
    A standard error is to think that because a word is used to refer in NL, 
    that what it refers to must be a basic or primitive individual.  For 
    temporally embedded 'things', this is almost always a mistake. The 
    logically primitive things in examples like yours are not people, but 
    people-at-a-time. People last for a while and change their properties: 
    they are complex entities. The 'conceptual' atoms suggested by informal 
    usage are usually not the best logical atoms to try to build an ontology 
    out of.
    That's one way to look at it.  But it is not the only way. 
    This is the case for
    relations such as "Person buys Product from Vendor" or "Person kisses 
    while it is not the case for relations such as "Point1 is between Point2 
    and Point3"
    How about if Point2 is defined in a spatial reference frame which is 
    attached to a moving vehicle? Perhaps you do not accept such things as 
    truly points; but they can be points in the topological sense. And if you 
    reject these as points then you seem to be assuming a global spatial 
    reference frame, which has been known to be physically meaningless since 
    Einstein stated special relativity.
    Yes, indeed.  The distinction is entirely subjective.
    or "Person is taller than Person" (the latter is a relation between the 
    heights of two persons, being qualities in the underlying "conceptual 
    according to the theory of Peter Gärdenfors presented in his book 
    Spaces: the Geometry of Thought", 2000).
    Regarding the last example, I think you are confusing 'person is taller 
    than person' (where the 'person's refer to continuants) with 'the height 
    of person is greater than the height of person', interpreted at a moment 
    in time.
    However, thanks for clarifying which of the various possible philosophical 
    theories you are taking for granted. I take it then that you are proposing 
    to base the world's ontology standards on the work of Gardenfors?
    The idea of  ontological "features" or "moments" was something that you, 
    Fritz, and I discussed all night once in Maine.  And I don't think you 
    ever got it.  It would be difficult to explain how Gaardenfors stuff fits 
    into that picture if you can't see the picture.  However it is certainly 
    not the case that anyone I know proposes to "base" any ontology on it, it 
    is simply used in places in several ontological theories.
    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. 
    First, I do not accept that this is meaningful; but even if it were, it 
    does not answer the question: for I could rationally claim that any 
    relation, even a merely extensional relation, defined an intensional 
    relation (of which it was the extension). This would be consistent with a 
    philosophical position to the effect that all relations ultimately resided 
    in thoughts, for example, along with a rejection of simple mathematical 
    Platonism. It is also the position built into the Common Logic and RDF 
    formal semantics, by the way.
    I agree with Pat.  This holds no meaning to me, I really can't fathom what 
    is being referred to.
    ... 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! 
    Quite. And since they are not, there is reasonable scope for rational 
    people to disagree about them. 
    Let's get some of them involved in the discussion, then.
    Which is why any generally acceptable ontological framework cannot be 
    based on any of them. Certainly I personally will resist any attempt to 
    impose the GFO ideas on any reasoner that I have anything to do with. 
    (BTW, there are good engineering reasons for this declaration, not just 
    philosophical distaste. Though in fact I also believe that philosophical 
    distaste is quite a sufficient reason in itself.)
    Is that being proposed?  Hmmm...I think this could be an interesting 
    discussion, but I'm skeptical, too.  I can imagine special-purpose 
    reasoners that assume some ontological position in order to gain some 
    efficiency advantage, but in general it seems best to stick to logic.
    PS sorry if you are wondering why a casual remark has stirred up such a 
    hornets nest. I do have have rather strong feelings about attempts to 
    impose a 'correct' ontological framework, and react rather strongly to 
    assumptions that any such 'basic' framework should be accepted, 
    particularly on any kind of philosophical authority. If there ever were a 
    profession which is least likely to understand the way that world is 
    actually constructed - which , after all, is the original meaning of 
    'ontology' - then philosopher would be a good candidate. Having been a 
    philosopher (for a while), I am left with a deep-seated, almost religious, 
    conviction that almost all philosophy is either in fact logic, or else is 
    bad philosophy.  Certainly I will claim it as an objective, verifiable 
    fact that any nontrivial philosophical claim has been disputed by some 
    other philosopher, and that nothing is ever settled. Philosophy, unlike 
    science, does not make progress: it does not accrue knowledge, but simply 
    invents new arguments.
    Excepting someone who is brilliant beyond the degree of anyone I've ever 
    met, like Shelock Holmes maybe, it is only through argumentation that we 
    truly come to understand what we really mean by our convictions and 
    beliefs.  It is a complete mistake to say that Philosophy does not make 
    progress, unless you think having a better understanding of what it really 
    means to believe something is not progress.
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