Re: [ontolog-forum] Prospects made into Customers and Vice Versa

[Thomas Johnston <tmj44p@xxxxxxx>]

<<<

Sets don't have universes of discourse: that notion arises in giving a semantics to a language (hence "discourse"). Do you mean, they are all subsets of a (large) set of possible values, like the domain and range of a function? 

No, I mean to say what I said. If a set consists of all people who have blue eyes, then the universe of discourse is all people, and the set membership criterion is "blue eyes". If the set consists of all of my customers, then the universe of discourse might be all adults, and the set membership criterion might be having applied for customer status and having a credit score of 750 or above. 

Translating those statements into a terminology that only mathematicians are comfortable using would not correct any mistakes in what I said, or indeed eliminate any ambiguities. (Please correct me if I'm wrong.) 

And with what assumptions do you correct me for using the terminology I did use? Is it that technical terms are each defined in a specific context, and that any use of them outside that context is inappropriate, or perhaps even wrong? If so, how do you draw boundaries that delineate those contexts, separating them from, for example, wider contexts which incorporate them?

> , and (b) the same "predicate" (as Stoll puts it), or "set membership criterion" as I would prefer to put it.

Well now, that can't be correct, because if they had the same membership criterion then they would be the same set. You must be referring to something else, and it would be very helpful to know what it is. Can you give an example? 

I agree that they would. Take a table with a set of 10 rows at time t. Delete one of those rows. The table now instantiates a different set of rows, at time t+n. Add back the deleted row. The table now instantiates the same set of rows it instantiated at time t+n. The same set has occurred twice, in a temporal sequence of sets.

I will make a guess, but forgive me if I get this wrong. There are individuals whose properties may vary with time. Let us write this using the convention that P(x, t) means that x has property P at time t. The (a?) "varying set" associated with P is the (a?) function S from times to sets such that for all t, S(t) is (a subset of?) {x: P(x, t)} . Is that more or less right? 

>>>

Your description is at a higher level of abstraction than mine is; for that reason, I consider it a less appropriate way of saying what I said than the exact language I used to say it. I was talking about tables and their sets of rows, and I think that what I said was both clear, correct, and well-suited for the context of the discussion.

> (v) The temporally-ordered sequence of those states, then, constitutes the life-history of that table. (This temporally-ordered sequence is not itself a set, because the same set may occur in the sequence at multiple non-contiguous periods of time.)

Does each state have an associated time (perhaps a time-interval)? If so, it would be both more natural and more useful to model this mathematically as a function from times to sets (=states). And, just as an aside, are you sure that a state of a table really is something as simple as a set? 

Are you sure that no sense can be made of referring to the state of a table that way? 

re your aside, it would take someone pretty simple to think that a table really is something as simple as a set. My own simple definition of a table is, roughly, that it is a type whose tokens are rows; that under a linguistic interpretation, those rows are declarative sentences within a Gricean context; that all orthographically identical rows are sentence tokens of the same statement; that under a logical interpretation, it corresponds to an existentially-quantified statement schema, and its rows to instantiations of that schema; that under an ontological interpretation, it is an Aristotelian secondary substance and its rows are Aristotelian primary substances. I have also given a relational + type/token + linguistic + logical + ontological interpretations of columns of relational tables (in Chapter 5 of my second book).

I'll look forward to any corrections you may have, but at that point, I'm going to stop communicating with you. There has been only one other author in my life with whom communication has been, for me, this tense. For my part, the tension I feel with you and this other author is based on the anticipation that whatever I write will be interpreted so as to make me look as foolish as possible. I always write on the basis of assuming that the other party is intelligent, and that if I don't fully understand him, that perhaps a little effort on my part will enable me to make him out to be something other than completely uninformed. With you and the other party I alluded to, this conversational stance of mine puts me at a real disadvantage.

Everyone expresses themselves in their own idiolect (a tautology, of course). Here in this forum, our idiolects hopefully coalesce on a dialect whose subject matter is databases, logic, semantics, ontology, and related concepts. If the idiolect I use seems as unintelligible, or perhaps just simply wrong, to others in this forum as it apparently does to you, then my only self-respecting course is to withdraw from this forum.

But I don't like conversing with people who make me look stupid because, for the most part, I don't think I am stupid.

Regards, and regrets,

Tom Johnston

On Tuesday, October 27, 2015 6:21 PM, Pat Hayes <phayes@xxxxxxx> wrote:

On Oct 27, 2015, at 4:06 PM, Thomas Johnston <tmj44p@xxxxxxx> wrote:

> Response to Pat's Comment
>
>
> Are there time-varying sets, in the sense of sets whose membership varies over time? Of course not. And so, although I never said that the term "time-varying set" referred to the notion of a set whose membership varied over time, it is certainly easy to read the term that way. So I spoke carelessly, and I apologize for that.
>
> I seem to recall adopting the term "time-varying set" from Chris Date. That doesn't legitimate the term, but it may explain why it came to mind as I wrote my comment. And the fact that an important author in the field of relational databases also uses the term suggests that there is something that he, like I, think that the term might usefully be referring to.
>
> In my case, as indicated in my reply to John Sowa in this same thread, I think the term is a reasonable one to be used to refer to a specific temporal sequence of sets. The idea is that each transformation of (update to) a relational table puts that table in a new state; and it is each of those states that is a set, and the temporal sequence of those sets that I used the term "time-varying set" to refer to.
>
> I expressed this idea much more clearly in my reply to John Sowa in this thread, written at close to the same time as my reply to Pat. Here's a summary statement of what I said:
>
> (i) A table in a relational database is a time-varying object.
>
> (ii) A transformation to the contents of a table (i.e. an insert, update or delete) replaces the current state of the table with a different state.
>
> (iii) Each of those states is a set – specifically a subset of the Cartesian Product of the ordered set of sets which makes up the columns of the table.
>
> (iv) At any point in time in the life-history of a table, it is in one and only one state; it physically realizes one and only one set.
>
> (v) The temporally-ordered sequence of those states, then, constitutes the life-history of that table. (This temporally-ordered sequence is not itself a set, because the same set may occur in the sequence at multiple non-contiguous periods of time.)

Does each state have an associated time (perhaps a time-interval)? If so, it would be both more natural and more useful to model this mathematically as a function from times to sets (=states). And, just as an aside, are you sure that a state of a table really is something as simple as a set?

> (vi) I used the name "time-varying set" to refer to that temporal sequence of sets.

It would be much simpler if you didn't, though :-)

> (vii) What relates the sets in each of these "time-varying sets"? If we use the Principle of Extension, I don't see a straightforward answer to the question. But if we use the Principle of Abstraction, the answer is that the sets in a "time-varying set" are related by having (a) the same universe of discourse

Sets don't have universes of discourse: that notion arises in giving a semantics to a language (hence "discourse"). Do you mean, they are all subsets of a (large) set of possible values, like the domain and range of a function?

> , and (b) the same "predicate" (as Stoll puts it), or "set membership criterion" as I would prefer to put it.

Well now, that can't be correct, because if they had the same membership criterion then they would be the same set. You must be referring to something else, and it would be very helpful to know what it is. Can you give an example?

I will make a guess, but forgive me if I get this wrong. There are individuals whose properties may vary with time. Let us write this using the convention that P(x, t) means that x has property P at time t. The (a?) "varying set" associated with P is the (a?) function S from times to sets such that for all t, S(t) is (a subset of?) {x: P(x, t)} . Is that more or less right?

> As an aside I also note (since this topic is one I have worked on for a long time), that the standard (ISO 9075:2011 and/or TSQL2) theories of bitemporal data include the notion that there are two "time-varying sets" (in this sense) corresponding to each table, one tracking the temporally-ordered change of state of the objects represented by rows in each table, and the other tracking the temporally-ordered change of state of each table itself.

That sounds like the distinction between vlaid and transaction time(?). To properly model this requires having a more nuanced model of time.

Pat

> With this interpretation of the phrase "time-varying set", and with relational database tables being the original topic under discussion, my original point can be rephrased like this: a relational table is a "time-varying set" (i.e. a temporal sequence) of table states, each state being a specific collection of rows. By the Principle of Abstraction, what each of those states has in common is that they are defined on the same universe of discourse (a Cartesian Product of sets) and use the same set membership criterion.
>
> And I once again apologize for using a term which originally seemed innocuous enough, but which I now realize is more naturally understood the way Pat understood it – as an oxymoron. I will henceforth try to use some such term as "temporal sequence of table states (sets)".

>
>

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