RE: SWRL (FOL) n-ary relations

From: Pat Hayes (
Date: 01/18/05

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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.
    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 
    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?
    >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 
    >[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.
    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.
    >So, yes there is a practical reason for making
    >this conceptual distinction.
    There might be if that analogy made sense.
    >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 necessary.)
    >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. 
    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.
    >An attempt to characterize the difference between
    >those formal relations and other relations
    There are no such differences.
    >  (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. 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. 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. 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. 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 
    relations. 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.
    >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"
    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.
    >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).
    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?
    >...; 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. 
    Thanks for clarifying that interesting piece of 
    academic politics: I had wondered why Barry had 
    left the place so soon after going there with 
    such fanfare (I was visiting Buffalo when he was 
    shortly to depart for Leipzig).  However, it was 
    the GFO and GOL that I was referring to, in fact. 
    I have separate disagreements with Barry's 
    ontological views, and you and I may well agree 
    on those.
    >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.
    >... 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* 
    >[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. 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.)
    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.
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