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

To: "'Pat Hayes'" <phayes@xxxxxxx>
Cc: "'[ontolog-forum] '" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "Chris Partridge" <mail@xxxxxxxxxxxxxxxxxx>
Date: Fri, 16 Mar 2007 17:59:25 -0000
Message-id: <015501c767f4$d5912990$6a00a8c0@Aegir>
Hi Pat,    (01)

To the most important point.    (02)

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.     (03)

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)    (04)

PH>And the ISO Common Logic standard, and the associated papers on its
background by Chris Menzel and myself.    (05)

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.)    (06)

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).    (07)

I have put other comments in-line below.    (08)

Chris    (09)

-----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
Metaphysics    (010)

>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.    (011)

More predicates then properties? I would have 
guessed the reverse: certainly in any real HO 
semantics the reverse will be true.    (012)

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.    (013)

>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
>universals    (014)

Can you give me an example? I confess to not following what you mean.    (015)

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.     (016)

>(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.    (017)

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 :-)    (018)

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'.     (019)

>The second is that the predication relation is not really accessible - and
>have found that it is useful to have this. In Barry Smith's terms - if you
>start with Fa - you have nothing explicit in your notation for the link
>between F and a.    (020)

Well, not so far, you can easily put it there. 
That is what DLs do, in effect. Here's the 
relevant part of the RDF-CL embedding, written in 
CLIF:    (021)

(forall (F a)(iff (F a)(rdf:type a F)))    (022)

where rdf:type is the RDF name for the unary 
predication relation. And yes, this really is 
first-order.    (023)

>  I am sure you can dig up papers on the varieties of
>predication, exemplification etc. which give a more theoretical position on
>I also find it odd to think of the subsumption (subtype/subclass) relation
>as a kind of material implication (Fa -> Fb) - as seems to happen with some
>FOL ontologies.    (024)

Some, but not all. The CL position (also used in 
RDFS, but not OWL) is that subsumption implies, 
but is not identical to, the subset relationship 
expressed by material implication. Not only is 
this first-order, it gives a much more tractable 
logic, by eliminating the contrapositive case of 
the extensionality assumption which is almost 
never needed in practical reasoning.    (025)

>I realise that one can regard properties and universals as the range of the
>FOL variables (see Andrew Newman's The Physical Basis of Predication - as
>well as Barry's Fantology paper)    (026)

And the ISO Common Logic standard, and the 
associated papers on its background by Chris 
Menzel and myself.    (027)

>. I have been told that there are problems
>with this in terms of the categoricity of models (I'll let you or ChrisM
>explain this).
>So, I suppose that if you drop the predicate-property assumption, then FOL
>becomes ontologically bland. But I am not sure that is the way people want
>to go. It seems to me that a number of the inference engines have this
>assumption built in.    (028)

The inference engines take what we give them. If 
they only ever see a 'holds' or 'type' 
predication, then that is all they have to work 
with. True, many of the resolution engines will 
become inefficient if they are not given a rich 
collection of predicates, as they are written 
using these names as hashing codes. But this 
really is only an accident of a certain coding 
style, rather than anything fundamental.    (029)

>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).    (030)

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.    (031)

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.    (032)

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. 
CP>This goes back to my question about the relationship between inference
and ontology. I was hoping ChrisM was going to point me towards a corpus of
work where this is clearly described. As I said in one of my mails, it seems
to me that there is, in some cases, something like an ontological dependence
implied by some inferences. But how to systematise this insight - if indeed
it is an insight.    (033)

>If that is what the empirical
>data tells us, we should listen.
>If I may put this another way (and bring it back to the title of the post),
>if you are making claims about FOL in terms of logic/inference, I do not
>disagree. If you are making claims about ontology/existence - through the
>structure of FOL - then it seems to me that there are examples where FOL is
>not neutral.    (034)

Well, I stand by my position. I will admit that I 
am understanding 'first-order' in a way that may 
differ from some textbooks, although not from a 
large body of semantic work in the last few 
decades. I will use CLIF as my standard FO 
notation.    (035)

>And, I think it would make things a lot easier if we had a better
>explanation of the links between inference/logic and ontology (in the
>philosophical sense).    (036)

As a slight straw man, or at least a man with 
straw in his hair, I will start the discussion by 
claiming that there is no link between them at 
all; that FOL is entirely ontologically neutral 
in the sense that any ontological position can be 
expressed by writing FO sentences. I invite 
attempts at refutation :-)    (037)

Pat    (038)

>-----Original Message-----
>From: Pat Hayes [mailto:phayes@xxxxxxx]
>Sent: 16 March 2007 15:37
>To: Chris Partridge
>Cc: [ontolog-forum]
>Subject: Re: [ontolog-forum] The Relation Between Logic and Ontology in
>>Chris, John,
>>The topic itself seems to me interesting.
>>You may be able to shed some light on this.
>>>From what little I know, it seems as if at the beginning of the 20th
>>century, philosophical opinion tended towards regarding logic as a
>>candidate for ontology. By the end of the century, ontology is about what
>>exists and logic about what can be inferred.
>>It seems to be the case, as noted below, that "ontological considerations
>>might play a role in the choice of an appropriate formalism"  and
>>that a formalism (such as FOL) might have implicit ontological
>Hmm. I wish ChrisM has not agreed to this quite
>so readily. I think this dictum, while of course
>defensible, can be very misleading if understood
>too strongly, as a kind of Whorfian view of
>logic. All the formal and I would suggest
>informal evidence seems to point to FOL, in some
>incarnation, as the single best 'ontologically
>neutral' logic. This is because the *only*,
>repeat ONLY, assumption that FOL makes about its
>universe is that is is a nonempty set (and if you
>are willing to live with a free logic, which Im
>not, you can even allow it to be empty). And,
>moreover, it is the ONLY logic which does make
>only this minimal assumption. All other logics
>seem to impose extra conditions on their
>universes: HOL requires it to be closed under
>relational comprehension, modal and context
>logics require it to support some kind of
>neo-Kripkean structure, etc.. Now, it is hard for
>me to image what could possibly be *less* of an
>ontological commitment than that the elements of
>the universe can be viewed as members of a set:
>this is almost a prerequisite for *any* kind of
>thing that can possibly be describe
>mathematically, i.e. using the apparatus of a
>modern precise semantic theory. So FOL - again,
>understood model-theoretically, so the term can
>encompass quite a wide variety of actual logics -
>seems to me to be as ontologically bland, as
>ontologically un-Whorfian, as it is possible for
>a logical framework to get. MOreover, virtually
>all the various alternative formalisms that have
>been suggested for serious ontology use can be
>easily transliterated back into FOL or a suitable
>FOL theory (eg for modalities one needs to
>introduce possible worlds, aka states, aka
>situations, aka contexts, and quantify over them
>in an appropriate way.) Can we all simply agree
>on this, and move forward? We have serious
>engineering points to get solved, and it is very
>discouraging to find ourselves debating and
>re-debating issues that were interesting in
>technical philosophy a century ago but which have
>been laid to rest in every practical sense for
>about 30 years now.
>>I wonder whether either of you (or anyone else on the list) could point to
>>philosophical research on the links between the two.
>>One thing that puzzles me, for example, is whether something like an axiom
>>that states the whole-part relation is transitive is implying that there
>>some kind of ontological dependence between the parental and ancestral
>>whole-part relations.
>Say what you mean by 'ontological dependence'.
>That axiom certain asserts that there is an
>inferential connection between them: it allows
>you to infer statements involving one of them
>from statements involving the other. Is this an
>'ontological dependence'?
>>And if so, why? And under what conditions does
>>inference imply ontological dependence?
>I have no idea, because I don't know what the second phrase means.
>>Why is this interesting? Well, understanding it may help us in choosing
>Lets just choose (your favorite subset of) FOL,
>and move forward. Everyone else does, whether
>they admit it or not.
>>-----Original Message-----
>>From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx
>>[mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of John F. Sowa
>>Sent: 16 March 2007 13:44
>>To: [ontolog-forum]
>>Subject: Re: [ontolog-forum] The Relation Between Logic andOntology in
>>Fine.  We can all agree on that:
>>   > I certainly agree that ontological considerations might
>>   > play a role in the choice of an appropriate formalism.
>>And the converse is also true:  the formalism can affect
>>or bias the choice of ontological categories and the
>>way they are developed, studied, and used.
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40 South Alcaniz St.    (850)202 4416   office
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