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Re: [ontolog-forum] The Relation Between Logic and Ontology in Metaphysi

To: "Chris Partridge" <mail@xxxxxxxxxxxxxxxxxx>
Cc: "'[ontolog-forum] '" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Pat Hayes <phayes@xxxxxxx>
Date: Fri, 16 Mar 2007 14:10:55 -0500
Message-id: <p06230911c220974f13dc@[]>
>Hi Pat,
>To the most important point.
>If I read you correctly, you do not subscribe to the notion that one should
>equate the predicates in FOL with properties/universals in the ontology.    (01)

Not *equate*, no. The correspondence between logical categories of 
symbols, and ontological categories of concepts, is ours to determine 
as we see fit. We are the ontology engineers. In any case, in CL and 
its variants, there is no syntactic distinction between predicates 
and other names.    (02)

>CP>I realise that one can regard properties and universals as the range of
>>FOL variables (see Andrew Newman's The Physical Basis of Predication - as
>>well as Barry's Fantology paper)
>PH>And the ISO Common Logic standard, and the associated papers on its
>background by Chris Menzel and myself.
>However, can I assume that you would agree with the point that if someone
>were to insist on saying that all universals/properties MUST be coded up as
>predicates in FOL, there would some ontological implications - and some loss
>in expressivity? (This was my main point.)    (03)

Oh sure. But the problem there is not the use of FOL, but (if I may 
descend to an unworthy adhominem) adherence to an oversimplified 
doctrine, or possibly a failure of imagination :-)    (04)

>BTW I hope it is clear I was NOT trying to make an argument for HOL or
>against FOL in general (as a form of logic/inference).
>I have put other comments in-line below.
>-----Original Message-----
>From: Pat Hayes [mailto:phayes@xxxxxxx]
>Sent: 16 March 2007 17:11
>To: Chris Partridge
>Cc: '[ontolog-forum] '
>Subject: RE: [ontolog-forum] The Relation Between Logic and Ontology in
>>Hi Pat,
>>May I check out one of your claims? I know we may well be going over old
>>PH>This is because the *only*, repeat ONLY, assumption that FOL makes about
>>its universe is that is is a nonempty set
>>If we take the old early 20th century philosopher's view of logic as the
>  >language to express an ontology (strictly speaking - the language in which
>>to describe an ontology). This assumes some sort of link between predicates
>>and properties - where there may be more predicates than properties.
>More predicates then properties? I would have
>guessed the reverse: certainly in any real HO
>semantics the reverse will be true.
>CP> Agreed. I may have been sloppy - I meant that not all predicates are
>necessarily properties. (As I think you may have guessed.) Agreed the
>converse is also true.
>>Then I
>>think we find (at least two) awkward constraints.
>  >
>>The first, we have discussed before. The world seems (to me at least) to
>>have what I will call second order universals - i.e. universals of
>Can you give me an example? I confess to not following what you mean.
>CP>In an FX system you will have a file for the FX Deal Types. This will
>contains a number of records, e.g. Spot FX Deals and Forward FX Deals. The
>FX Deals file contains records of individual deals - which have a pointer to
>the FX Deals Type file. I would interpret this at that there are Spot FX
>Deals and Forward FX Deals and that these are instances of (the higher
>order) FX Deal Types. In my book, I offer the examples of Car Types that has
>Minis as an instance - where there are instances of minis - I also talk of
>Colours having individual colours such as Red and Green as instances.    (05)

Oh, I see. Yes, of course, I agree with you. In the language of 
recent SWeb standards debates, one has to allow classes of classes.    (06)

>>(I am not trying here to make a commitment to universals, call
>>them classes, sets, types or whatever is your poison). This can be
>>(impossible?) to describe properly in FOL.
>Depends on what you consider 'proper' :-)  There
>are all the negative results about FO
>expressibility, of course, but one can certainly
>do some describing of second-order entities in
>FOL. The question is whether or not this FO
>description is adequate. I think that it is, in
>all the cases I have seen. But we would have to
>get down to cases to make this go beyond an (is
>not/is so) conversation :-)
>CP>I suppose my question is that if one takes the position that properties
>can ONLY be described with predicates, how much of a workaround is needed to
>handle higher order universals/properties. How close does this come to what
>Copernicus described as 'such a monstrous system that it is impossible to
>conceive of God having constructed it'.    (07)

Sounds like ramified type theory. Well, I will admit that if one is 
obliged to write CLIF content in a traditional 'segregated' dialect 
syntax using 'holds/app', then these axioms do all look far more 
monstrous and far less easy to read. But then if you have to read OWL 
as OWL/RDF/XML, the same applies. A lesson I have drawn from the Sweb 
experience is that ugly surface forms sometimes have to be accepted 
as useful to machines rather than people. I think of the 'holds/app' 
translation not as being the 'real' axioms but rather as a 
longwinded, ugly (for people) but useful (for machines) 
transliteration of the real logical form.    (08)

>>BTW my concerns are not down to theoretical ontological squeamishness - I
>>find this has serious practical problems. In my 'reverse-engineering' of
>>ontologies from legacy systems, I find large tracts of the reference data
>>are irredeemably higher-order (universals).
>Irredeemably?? I am quite unconvinced that
>universals really need true semantic higher-order
>predication. That would be a very strong claim to
>defend. Are you sure that the cardinality of the
>set of universals is really uncountable? I am for
>example quite happy to admit the possibility of
>nonstandard models of arithmetic. Nothing
>ontological turns on such an admission.
>CP> Just to be clear. I am NOT suggesting that HOL is needed, merely that
>there are clearly higher order properties. I just raise the question of,
>giving that they exist, how you are going to accommodate them in your logic.    (09)

No problem. FOL can describe higher-order properties. What it can't 
do is quantify over ALL of them; there are just too many of them. OK, 
you can't do that; you can in fact only quantify over a countable 
subset of them. So, do that. I'll bet that will be enough for anyone 
but a mathematician.    (010)

>CP> I presume you would not want to sign up to an argument that goes like
>this. FOL is the answer. FOL does not allow higher order predicates, so
>higher order properties do not exist.    (011)

Quite, because its false to say FOL does not allow HO predicates. 
Take a look at, say,
http://www.ihmc.us/users/phayes/HayesMenzel-2001-KIF.ps (SKIF was an 
early draft of what is now the CL standard dialect CLIF)    (012)

Pat    (013)

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