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Re: [ontolog-forum] Ontology of Rough Sets

To: doug@xxxxxxxxxx, "[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Pat Hayes <phayes@xxxxxxx>
Date: Tue, 25 Jan 2011 03:24:17 -0600
Message-id: <F5322589-B123-4F12-AF92-2BE76C6E18E6@xxxxxxx>

On Jan 25, 2011, at 12:04 AM, doug foxvog wrote:    (01)

> On Sat, January 22, 2011 19:58, Pat Hayes said:
>> On Jan 21, 2011, at 10:57 PM, doug foxvog wrote:
>>> On Fri, January 21, 2011 13:39, Ed Barkmeyer wrote:
>>>> Christopher Menzel wrote:
>>>>> On Jan 21, 2011, at 9:46 AM, doug foxvog wrote:
>>>>>> ...
>>>>>> A standard distinction between a set and a class, is that membership
>>>>>> in a [set] cannot change, while membership in a class can.
>>>>> I think it's useful to distinguish two claims when it comes to the
>>>>> identity conditions of classes:
>>>>> (1) Classes are not extensional (i.e., distinct classes can have the
>>>>> same members/instances)
>>>>> (2) Classes can change their membership.
>>>>> In the formal semantics of a number of KR languages, (1) is true but,
>>>>> strictly speaking at least, (2) is not.  Notably, classes in OWL are
>>>>> explicitly non-extensional: since a class is stipulated only to *have*
>>>>> an extension in OWL's formal semantics, nothing prevents distinct
>>>>> classes from having the same extension.  The same is true of RDF.
>>>>> However, simply because there is no formal notion of change built into
>>>>> OWL's semantics, there is no possibility, within a given
>>>>> interpretation,
>>>>> that a class change its membership.  As noted in an earlier message in
>>>>> this thread, without augmenting the notion of an OWL interpretation
>>>>> somehow, change can only be represented formally in terms of something
>>>>> like a series of interpretations that are thought of as temporally
>>>>> ordered.  That said, (2) does seem to be a strong *intuitive* idea in
>>>>> the KR, AI, and database communities.
>>>> The particular problem I have recently got involved in is the intrusion
>>>> of temporal concepts into would-be ontologies in business applications.
>>>> In the supply-chain area, for example, it is important to be able to
>>>> talk about schedules and shipments being "late".  Getting past the
>>>> indexical issues, which are fixed by translating the intuitive "now"
>>>> into specific time relationships, the particular problem is that
>>>> shipments and orders do change state, and actions are taken on the
>>>> basis
>>>> of reclassification.
>>> Fine.
>>>> A major problem for us is that the industry folk throw these concepts
>>>> into what was an ontology for the "snapshot" model of decision-making
>>>> --
>>>> the state of the world at the time the decision is to be made.  This
>>>> gives rise to formalizing ideas like "proposition X is false at time A
>>>> and true at time B."  And that problem arises from the idea that states
>>>> of things are characterized by propositions, which seems to be
>>>> fundamental to applications of ontologies.
>>> This is fine for representing states.
>>>> The 4D idea that a thing in a different state is a different thing,
>>> What is the need to consider a thing in a different state a different
>>> thing?
>> It has many advantages over time-state-based ontological frameworks,
>> though it also (of course) has its problems. The chief advantage can be
>> summed up as its ability to talk about things at different times in the
>> same sentence. for example, it is much easier to define notions such as
>> rate of change if one is able to talk about temporal 'slices' explicitly.
> Sorry, i misinterpreted.  By "thing in a different state", you mean a
> time slice of a thing when it is in that state.  Yes, in 4D, a time slice
> of a 4D worm is a different thing than the full 4D worm.  It holds the
> relationship with the full worm (or some encompassing time slice) as
> being a temporal part of the larger thing.
> I thought you meant that a (temporal) thing, during a time period when it
> has a specific state, is a different thing.  The complete 4D object is
> the same 4D thing at any time, whether that time intersects the object
> or not.      (02)

I think we are in violent agreement, but I would suggest that your way of 
expressing yourself here is potentially misleading. (It misled me, at least.) 
If we are talking 4D, then the usage "same thing at a time" is not strictly 
correct, since 4D assertions are not made AT a time, but are themselves 
timeless, like statements of mathematics. This usage suggests the axiomatic 
style in which one refers to 3D objects and times separately, and writes things 
like In(Pat, Florida, Jan2011) where Pat is understood to refer to a 3D 
continuant, and it makes sense to write time-indexed identity assertions such 
=(Barack_Obama POTUS 2010)    (03)

> That 4D object can have different states at different times;    (04)

Er... no, it can't. It has temporal slices or parts, sure. But it - the 4D 
entity - does not have anything 'at different times'. It has properties, and 
stands in relations, which are themselves not temporally indexed at all; indeed 
it would be logically incoherent to temporally index them. That is the whole 
point of introducing 4D entities in the first place.     (05)

> and those states also adhere to temporally intersecting temporal slices
> of the object.
>> The issue is not what counts as a 'thing', but whether one is allowed to
>> talk of temporal slices - things-in-a-state - as entities in the ontology
>> at all. (Could there be a class of them, for example?)
> In 4D, there certainly be such classes.
>> Opponents of the 4D
>> approach typically reject such entities as incoherent, philosophically
>> confused, etc..
> Agreed.
>>> This is not what the ontological community considers to be a 4D idea.
>> It is exactly that.
> A temporal slice as a separate thing is certainly a 4D idea.    (06)

Right.    (07)

>  The idea
> that a 4D object can not have different states at different times is
> not a 4D idea.    (08)

I disagree. This is a foundational part of the 4D approach, that assertions 
about the spatiotemporal entities are not themselves temporally indexed. So 
they don't have different properties *at different times*. What they have is 
temporal parts which have (possibly different) properties; but this is not the 
same thing. In fact, the difference is exactly what distinguishes the 4D 
approach from the 3D-continuant approach.     (09)

>  I was referring to the second of these concepts, while
> you were referring to the first.  You are, of course, correct for what
> you are referring to.
>>> A 4D object, in this context, is an object that can have different
>>> state at different times.
>> No, that is a continuant.
> A continuant also has such properties.    (010)

A continuant is 3D, and has no temporal parts. It has different properties at 
different times. It is not extended in time, but rather it continues to exist 
as time passes. It is identically the same thing at one time as it is at 
another. In order to describe it, it is usually necessary to qualify all 
assertions with a time parameter.     (011)

A 4D object does have temporal parts, is extended in time, and exists only in 
the way that other things exist, by 'occupying' time and space. It does not 
have properties 'at a time'; it simply has properties, atemporally. It is 
described without using any temporal parameters.     (012)

They are not the same. Personally, I find it very hard to even imagine what a 
continuant is supposed to be, but some people find them very agreeable.     (013)

>> In a very strict 4D model, there is no single
>> 'thing' that has the various states. (Although I hasten to add, it is very
>> convenient to be somewhat less strict than this. I mean only to make the
>> conceptual distinction.)
> As someone else has mentioned, this depends upon your 4D model.  However,
> just as a static description of a 3D object can state that different
> spatial parts of the object have different attributes (or states), an
> appropriate ontology can describe different temporal parts of a 4D model
> as having different attributes (or states).    (014)

Attributes, yes, but not states. The states are what would have the attributes 
in a 3D ontology. They are not the attributes themselves.    (015)

>>>> and 'objects' are actually
>>>> sequences (or more generally, lattices) of things in states,
>>> This is a different model, that has a far different definition of
>>> "thing" than is generally used in computer ontologies.
>>>> is a means of producing a formal semantics,
>>> One could certainly produce a formal semantics using such definitions.
>>>> but it is totally out of line with the
>>>> intuition of the domain experts.
>>> Then it is probably not worth while to present such a model to them.
>>> If you want to use it "under the covers"/"inside the black box",
>>> because it makes calculations easier, fine.  But don't inflict such
>>> a model on domain experts.  I would suggest it also be hidden from
>>> the ontology builders and merely be maintained as part of the inference
>>> engine.
>> But the engine will be using the concepts provided by the ontology itself.
> Of course.    (016)

Then the ontology builders will surely need to be involved... 
>>>> They cannot then "validate" the
>>>> ontology -- they don't understand it.
>>>> I have said in that forum that solving the problem is beyond my
>>>> expertise.  It is my conviction that the problem is not really "time",
>>>> but rather "change of state" or "alternative states", and in that
>>>> sense,
>>>> "time" is a means of labeling "alternative possible worlds".
>>> Time is certainly one way of marking alternative states.
>>>> All we are saying is that the intuitive notion of change is endemic to
>>>> a lot of ontology applications.
>>> Certainly.
>>>> We can usually constrain the immediate application
>>>> to avoid the problem or create a convenient work-around,
>>> If you are only using the data with a single reference time period,
>>> the of work-around need not consider viewing the data in another
>>> temporal context.  But if the data is to be dealt with for another
>>> time period, that should affect the work-around method chosen.
>> The very use of terms like 'temporal context' suggests that you have
>> already chosen one way to handle the ontological description of time and
>> change. Which of course is fine, but you should acknowledge that others
>> prefer a different ontology, and that yours is by no means the only one
>> possible.
> By suggesting that a temporal context can be used in certain
> circumstances, i in no way am claiming that one must always be used to
> handle time and change, or that other sorts of contexts are not useful.
> Other methods of dealing with time and change are certainly valid,
> whether or not they deal with contexts.    (017)

Perhaps I was reading too much into the word "context". In formal KR work, the 
term has come to be used to indicate a particular style of formal description, 
in which all assertions are made relative to a 'context'. In effect, this 
attaches the temporal parameter to an entire sentence rather than to an object 
or an attribute. The resulting formalisms are IMO extremely awkward and 
cumbersome, and if anything represent a backward step. Applied to temporal 
descriptions, it amounts to using a tensed modal logic rather than a 4D 
description.     (018)

Perhaps this is not what you intended, however.     (019)

> I was suggesting that if one is using data from a single reference time
> period, a temporal context would be appropriate.  My next sentence
> suggested that when this is not the case, other alternatives should be
> considered.  I fail to see that in this i have prejudged how to handle
> ontological descriptions of change and time.    (020)

I took you to be suggesting the use of a context logic. As I say, this may have 
been a mistake on my part: apologies if so.    (021)

> Your reference, ``"time" is a means of labeling "alternative possible
> worlds"'', suggested to me that such "possible worlds" could (not "must")
> be mapped into contexts.  I am not suggesting that you intended this.
> One can reason about relationships among multiple possible worlds
> by stepping outside those worlds.  One can reason about relationships
> among multiple contexts by stepping outside those contexts.    (022)

Honestly, I have no idea what you mean here by a 'context'. I would be 
interested to know what you do mean. (One of my hobbies is collecting senses of 
the word "context". So far I have about 25 of them. :-)    (023)

Pat Hayes    (024)

> -- doug foxvog
>> Pat Hayes
>> ------------------------------------------------------------
>> IHMC                                     (850)434 8903 or (650)494 3973
>> 40 South Alcaniz St.           (850)202 4416   office
>> Pensacola                            (850)202 4440   fax
>> FL 32502                              (850)291 0667   mobile
>> phayesAT-SIGNihmc.us       http://www.ihmc.us/users/phayes
> =============================================================
> doug foxvog    doug@xxxxxxxxxx   http://ProgressiveAustin.org
> "I speak as an American to the leaders of my own nation. The great
> initiative in this war is ours. The initiative to stop it must be ours."
>    - Dr. Martin Luther King Jr.
> =============================================================
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IHMC                                     (850)434 8903 or (650)494 3973   
40 South Alcaniz St.           (850)202 4416   office
Pensacola                            (850)202 4440   fax
FL 32502                              (850)291 0667   mobile
phayesAT-SIGNihmc.us       http://www.ihmc.us/users/phayes    (026)

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