Re: [ontolog-forum] A Question About Mathematical Logic

[Thomas Johnston <tmj44p@xxxxxxx>]

Rich,

Like an earlier comment, yours emphasizes, I believe, the need to discuss (i) the difference between formal ontology and ontology engineering (which is roughly the difference between theory and practice), and (ii) the problems that arise when ontology engineers finding themselves having to do ontology, rather than having to just plug uncontroversial mini-ontologies into some well-defined framework (like Protege) or into a framework/template toolkit like OWL/RDF. I intend to do this in a new thread, and soon.

I have seen several remarks, by the engineers among us, about ontology and semantics being irrelevant to the work they do, being irrelevant, as you put it, to "real engineering problems". But I have also seen the confusion engineers create when they work with anything other than uncontroversial ontology fragments, e.g. a company's product hierarchy. 

As an ontologist, and a person somewhat familiar with systems of logic, I nonetheless appreciate the importance of getting ontologies into frameworks. That, in my opinion, is what puts the semantics in the Semantic Web -- it gives automated systems, doing cross-database queries, the ability to understand cross-database semantics. (Pat Hayes to correct me, please, if I'm off course here.)

An example I have come across in every one of two dozen enterprises I have worked for, is the question: "What is a customer?", where that question, more fully, means "What does your enterprise take a customer of yours to be?" I have never found subject matter experts who have been able to answer that question, without a good deal of help from me. And the help I provide is help in doing ontology clarification work, not help in plugging lexical items representing ontological categories into an ontology tool. Moreover, I have never found two enterprises whose experts defined "customer" in exactly the same way.

From which it follows that a cross-database query that assumes that two tables named "Customer Table", in two different enterprise's databases, are both about customers, is almost certain to be mistaken. Both tables may be about fruit, but there is certain to be an apples and oranges issue there. 

A formal ontology which includes customers, on the other hand, might be able to distinguish apples from oranges if it could access an ontology framework about customers. Given that the concepts have been correctly and extensively-enough clarified, here is where the ontology engineer proves his worth. 

But to define the category Customer clearly enough, it isn't engineering work that needs to be done. It's the far more difficult (in my opinion) ontology clarification work that needs to be done. (I expand on this example in the section "On Using Ontologies", pp. 73-74 in my book Bitemporal Data: Theory and Practice. I think I also elaborated on it a few weeks or months ago, here at Ontolog.)

So I think that engineers who suggest that clarifying ontological categories is irrelevant to their work as ontology engineers, are mistaken. Such work seems mistaken to them, I think, because most of the ontologies they put into their well-defined frameworks are relatively trivial, i.e. are ontologies that subject matter experts have no trouble agreeing on. The lower-level the ontologies we engineer, the more that will tend to be the case. 

But ascend into mid-level or upper-level ontologies, and ontology engineers get lost, and don't know how to find a clear path through the forest whose trees are those categories. And so instead of admitting "We're lost", they say instead "We strayed into a swamp that has nothing to do with the real engineering work we do -- which turns out to be the relatively straightforward work of plugging labels for uncontroversial ontological categories, and taxonomies thereof, into Protege or its like". 

I say, on the contrary, that conceptual clarification work in mid- and upper-level ontologies have everything to do with ontology engineering, and are where the really difficult work of that engineering is done. An analogy: machine-tooling parts is the hard work of manufacturing; assembling those parts is the easy work.

And my apologies to Leo, Pat and other whose comments on my question I have not yet responded to. I will, and soon. And I thank them and all other respondents for helping me think through the question I raised.

Tom

On Tuesday, October 13, 2015 12:52 PM, Rich Cooper <metasemantics@xxxxxxxxxxxxxxxxxxxxxx> wrote:

Although the approach you are suggesting might entertain some philosophical questions, and therefore be entertaining to philosophers, it has little or no relevance to real engineering problems, which almost never are applied to the actual universe of every possible entity - i.e. infinite supplies.

 

In engineering applications, Ex(...) would normally apply only to finite sized, or traversably infinite sized, problems.  The importance of scope in engineering, i.e., where you draw the lines around what is a system, which contains all the entities, enumerators of variables, constants and functions in real problems. 

 

Even unbounded engineering problems have limits to the possible types that can be used, though mechanisms like stacks, or even Turing machines with infinite square supplies, attempt to approximate boundless sizes. 

 

So I suggest your title should be A Question About Mathematical Logic, since engineers who consider themselves logic designers would find the ideas impractical, though linguists might be more interested.  

 

Sincerely,

Rich Cooper,

Rich Cooper,

 

Chief Technology Officer,

MetaSemantics Corporation

MetaSemantics AT EnglishLogicKernel DOT com

( 9 4 9 ) 5 2 5-5 7 1 2

http://www.EnglishLogicKernel.com

 

From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx [mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of Thomas Johnston
Sent: Tuesday, October 13, 2015 8:59 AM
To: Thomas Johnston; [ontolog-forum]; [ontolog-forum]
Subject: Re: [ontolog-forum] A Question About Logic

 

Paragraph 2 should read:

 

Suppose someone else asserts, instead, that "No dogs are renates". Certainly, to do that, that person must believe that there are such things as dogs and, in addition, believe that none of them are renates (a false belief, of course).

 

Sorry for the slip-up.

 

Tom

 

 

On Tuesday, October 13, 2015 11:57 AM, Thomas Johnston <tmj44p@xxxxxxx> wrote:

 

Oct 13, 2017.

 

My intuitions tell me that anyone who asserts "All dogs are renates" believes that there are dogs (i.e. is ontologically committed to the existence of dogs) just as much as someone who asserts "Some dogs are friendly".

 

Suppose someone else asserts, instead, that "No dogs are renates". Certainly, to do that, that person must believe that there are such things as dogs and, in addition, believe that some of them are not renates (a false belief, of course).

 

Now for "Some dogs are friendly", and also "Some dogs are not friendly". In both cases, we all seem to agree, someone making those assertions believes that there are dogs.

 

Now I'm quite happy about all this. If I make a Gricean-rule serious assertion by using either the "All" quantification or the "Some" quantification, I'm talking about whatever is the subject term in those quantifications – dogs in this case. I'm particularly happy that negation, as it appears in the deMorgan's translations between "All" statements and "Some" statements, doesn't claim that a pair of statements are semantically equivalent, in which one of the pair expresses a belief that dogs exist but the other does not.

 

But in the standard interpretation of predicate logic, that is the interpretation. In the standard interpretation, negating a statement creates or removes the _expression_ of a belief that something exists. My beliefs in what exist can't be changed by the use of the negation operator. Apparently, John's beliefs can, and so too for everyone else who feels comfortable with predicate logic as a formalization of commonsense reasoning, and with the interpretation of one of its operators as "There exists ....".

 

I usually don't like getting into tit for tats. Those kinds of discussions always are about trees, and take attention away from the forest. But I'll make exceptions when I think it's worth taking that risk (as I did in my response to Ed last night).

 

So:

 

From John Sowa's Oct 12^th response:

<<<  

TJ
> why, in the formalization of predicate logic, was it decided
> that "Some X" would carry ontological commitment

Nobody made that decision.  It's a fact of perception.  Every
observation can always be described with just two operators:
existential quantifier and conjunction. No other operators can
be observed. They can only be inferred.

>>>  

(1) If all ontological commitments have to be based on direct observation, then we're right back to the Vienna Circle and A. J. Ayer.

 

(2) And what is it that we directly observe? A dog in front of me? Dogs, as Quine once pointed out, are ontological posits on a par with the Greek gods, or with disease-causing demons. (I am aware that this point, in particular, will likely serve to reinforce the belief, on the part of many engineering types in this forum, that philosophy has nothing to do with ontology engineering. That's something I want to discuss in a "contextualizing discussion" I want to have before I pester the members of this forum with questions and hypotheses about cognitive/diachronic semantics. What does talk like that have to do with building real-world ontologies in ontology tools, in OWL/RDF – ontologies that actually do something useful in the world?

 

(3) I wouldn't talk about some dogs unless I believed that some dogs exist. And if some dogs exist, then all dogs do, too. Either there are dogs, or there aren't. If there are, then I can talk about some of them, or about all of them. If there aren't, then unless I am explicitly talking about non-existent things, I can't talk about some of them nor can I talk about all of them, for the simple reason that none of them exist. To repeat myself: if any of them exist, then all of them do.

 

(4) And I am, of course, completely aware that trained logicians since Frege have been using predicate logic, and that, at least since deMorgan, have been importing to negation the power to create and remove ontological commitment.

 

(5) Here's a quote from Paul Vincent Spade (very important guy in medieval logic and semantics):

 

"This doctrine of “existential import” has taken a lot of silly abuse in the twentieth century. As you may know, the modern reading of universal affirmatives construes them as quantified material conditionals. Thus ‘Every S is P’ becomes (x)(Sx ⊃ Px), and is true, not false, if there are no S’s. Hence (x)(Sx ⊃ Px) does not imply (∃x)(Sx). And that is somehow supposed to show the failure of existential import. But it doesn’t show anything of the sort .... "

http://pvspade.com/Logic/docs/Thoughts,%20Words%20and%20Things1_2.pdf

 

So Spade approaches this as the issue of the existential import of universally quantified statements. He points out that, from Ux(Dx --> Rx), we cannot infer Ex(Dx & Rx). The rest of the passage attempts to explain why. I still either don't understand his argument, or I'm not convinced by it. Why should "All dogs are renates" not be expressed as Ux(Dx & Rx)?

 

From John's reply, I think he would say that it's because we can only observe particular things; we can't observe all things. But in the preceding points, I've tried to say why I don't find that convincing.

 

(6) Simply the fact that decades of logicians have not raised the concerns I have raised strongly suggests that I am mistaken, and need to think more clearly about logic and ontological commitment. But there is something that might make one hesitate to jump right to that conclusion. It's Kripke's position on analytic a posteriori statements (which I have difficulty distinguishing from Kant's synthetic a priori statements, actually -- providing we assume that the metaphors of "analytic" as finding that one thing is "contained in" another thing, and of "synthetic" as bringing together two things first experienced as distinct, are just metaphors, and don't work as solid explanations).

 

All analytic statements are "All" statements, not "Some" statements. Kripke suggests that the statement "Water is H2O" is analytic but a posteriori. In general, that "natural kind" statements are all of this sort. Well, a posteriori statements are ones verified by experience, and so that would take care of John's Peircean point that only "Some" statements are grounded in what we experience.

 

I don't know how solid this line of thought is. But if there is something to it, that might suggest that if we accept Kripke's whole referential semantics / rigid designator / natural kinds ideas (cf. Putnam's twin earth thought experiment also), then perhaps we should rethink the traditional metalogical interpretation of "All dogs are renates" as Ux(Dx --> Rx), and consider, instead, Ux(Dx & Rx).

 

Well, two summing-up points. The first is that Paul Vincent Spade thinks that my position is "silly", and John Sowa thinks that it's at least wrong. The second is that such discussions do indeed take us beyond the concerns of ontology engineers, who just want to get on with building working ontologies.

 

As I said above, I will address those concerns of ontology engineers before I begin discussing cognitive semantics in this Ontolog (Ontology + Logic) forum.

 

Regards to all,

 

Tom

 

 

 

 

On Monday, October 12, 2015 10:49 PM, John F Sowa <sowa@xxxxxxxxxxx> wrote:

 

Tom, Ed, Leo, Paul, Henson,

TJ
> why, in the formalization of predicate logic, was it decided
> that "Some X" would carry ontological commitment

Nobody made that decision.  It's a fact of perception.  Every
observation can always be described with just two operators:
existential quantifier and conjunction. No other operators can
be observed. They can only be inferred.

EJB
> I was taught formal logic as a mathematical discipline, not
> a philosophical discipline. I do not believe that mathematics
> has any interest in ontological commitment.

That's true.  And most of the people who developed formal logic
in the 20th c were mathematicians.  They didn't worry about
the source or reliability of the starting axioms.

Leo
> most ontologists of the realist persuasion will argue that there
> are no negated/negative ontological things.

Whatever their persuasion, nobody can observe a negation.  It's
always an inference or an assumption.

PT
> on the inadequacy of mathematical logic for reasoning about
> the real world, see Veatch, "Intentional Logic: a logic based on
> philosophical realism".

Many different logics can be and have been formalized for various
purposes.  They may have different ontological commitments built in,
but the distinction of what is observed or inferred is critical.

HG
> I keep wondering if this forum has anything useful to offer the
> science and engineering community.

C. S. Peirce was deeply involved in experimental physics and
engineering.  He was also employed as an associate editor of the
_Century Dictionary_, for which he wrote, revised, or edited over
16,000 definitions.  My comments below are based on CSP's writings:

  1. Any sensory perception is evidence that something exists;
    a simultaneous perception of something A and something B
    is evidence for (Ex)(Ey)(A(x) & B(y)).

  2. Evidence for other operators must *always* be an inference:

    (a) Failure to observe P(x) does not mean there is no P.

        Example:  "There is no hippopotamus in this room"
        can only be inferred iff you have failed to observe
        a hippo and know that it is big enough that you would
        certainly have noticed one if it were present.

    (b) (p or q) cannot be directly observed.  But you might infer
        that a particular observation (e.g. "the room is lighted")
        could be the result of two or more sources.

    (c) (p implies q) cannot be observed, as Hume discussed at length.

    (d) a universal quantifier can never be observed.  No matter
        how many examples of P(x) you see, you can never know that
        you've seen them all (unless you have other information
        that guarantees you have seen them all).

TJ
> But now notice something: negation creates and removes ontological
> commitment. And this seems really strange. Why should negation do this?

The commitment is derived from the same background knowledge that
enabled you to assert (or prevented you from asserting) the negation.

> I'd also like to know if there are formal logics which do not
> impute this extravagant power of ontological commitment /
> de-commitment to the negation operator in predicate logics.

Most formal logicians don't think about these issues -- for the
simple reason that most of them are mathematicians.  They don't
think about observation and evidence.

CSP realized the problematical issues with negation, but he also
knew that he needed to assume at least one additional operator.
And negation was the simplest of the lot.  Those are the three
he assumed for his existential graphs.  (But he later added
metalanguage, modality, and three values -- T, F, and Unknown.)

John

PS:  The example "There is no hippopotamus in this room" came from
a remark by Bertrand Russell that he couldn't convince Wittgenstein
that there was no hippopotamus in the room.  Russell didn't go
into any detail, but I suspect that Ludwig W. was trying to
explain the point that a negation cannot be observed.

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