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Re: [ontolog-forum] Fwd: Ontologies and individuals

To: ontolog-forum@xxxxxxxxxxxxxxxx
From: Richard Dapoigny <richard.dapoigny@xxxxxxxxxxxxxx>
Date: Tue, 18 Dec 2012 15:11:30 +0100
Message-id: <50D07992.2080302@xxxxxxxxxxxxxx>
Hi all,
Le 18/12/2012 11:39, Pat Hayes a écrit :
> What is the purpose of this line of discussion? I for one have absolutely no 
>idea what "instance of" means, if it is something which is sharply distinct 
>from "member of" between an entity and a set of entities, and therefore have 
>no idea what sense of "individual" is being discussed here. But my larger 
>point is, what point is served by setting out to achieve any kind of consensus 
>on this matter?
>
> Suppose that such a consensus were to be achieved, so that we had a wide 
>agreement on a notion of individual and of what it means to be an instance of 
>a non-individual; still, the question reamins of how this is to be formalized 
>in a logical language.
>
> Logics come with a built-in notion of 'logical individual', which means, 
>things in the universe of discourse, ie things that the language quantifies 
>over, or assumes to exist. It would seem natural then to assume that when 
>formalizing this consensus, the way to proceed would be to design the logic so 
>that the universe of discourse comprises these individuals, and therefore 
>presumably excludes the non-individuals. In a classical FO language, these 
>non-individuals would be the properties and relations which apply to or hold 
>between the individuals, and then presumably "instance of" would be mirrored 
>by logical predication, so one would write (P a) to mean that a is an 
>"instance" of P. However, this elegant picture means that "instance of" must 
>be at least very similar to set membership, since the only extant semantics 
>for FOL treats predication as meaning set membership. This does not actually 
>require these two notions to be identical, but it does impose a very tight 
>constraint on what one might call logical similarity between them. To be 
>precise, "instance of" will be *logically indistinguishable* from set 
>membership: any way in which they are dissimilar will be invisible in the 
>logic itself; it will not be possible to state axioms in the logic which 
>capture this difference, whatever it may happen to be. As far as formal 
>ontologies are concerned, therefore, these differences between instance and 
>membership are irrelevant, and can (indeed, must) be ignored.
This is true as far as we consider set theory. The picture becomes 
different if we rather assume a type-theoretical framework. In that case 
"instance of" is formalized by the judgment  Gamma |- t : T read t "is 
of type" T. Alternatively, we can define a member in a social collection 
with the type MemberOf : SOB->SOB->Prop, where SOB is the type of social 
objects (or participants) and Prop the universe for logics. For example 
Musician : SOB is memberOf an Orchestra : SOB and if the predicate is 
true, then the type MemberOf(Musician, Orchestra) is proved.
Richard    (01)

>
> So perhaps we cannot simply identify individual with logical individual, but 
>must allow both individuals and non-individuals into the logical universe of 
>discourse, quantify over both of them, and have a sorting property 
>IsIndividual which allows us to assert Individual-hood of an entity:
> (IsIndividual x)
> Now we can, at least in principle, set out to write a formal ontology of 
>Individual-hood. Presumably, the relation instanceOf is also now in our 
>language, so we can write
> (forall ((x IsIndividual) y)(not (instanceOf y x)))
> which captures the suggested rule about individuals and instances, so is 
>plausibly an axiom of our nascent theory. (Any others?)
>
> But now we have partitioned our universe into two disjoint subsets. Why? What 
>useful expressive power have we achieved by having this distinction in our 
>ontology? Is it likely that there will be broad classes of things true of 
>things that satisfy IsIndividual which are not true of those that do not? Or 
>vice versa? If so, what kind of facts would these be? If not, what is the 
>purpose of making this distinction at all? What does it buy us? I submit that 
>until a clear answer is given to this question, we should not waste any 
>further time arguing over angels on pinheads.
>
> Pat
>
> On Dec 17, 2012, at 9:04 AM, doug foxvog wrote:
>
>> On Thu, December 13, 2012 11:55, Richard Dapoigny wrote:
>>> Hi all,
>>> I see that the debate about identification of individuals is far from
>>> being consensual.
>>> However, let us first (try to) agree of some fixed points as we say in
>>> mathematics.
>>> A usual definition is to see individuals as entities having no
>>> instance(s). Is there some agreement about this first definition?
>> This definition should be a little stronger (imho) -- to things that
>> conceptually can have no instances in any possible world.  This is a
>> feature of the thing being modeled, not of the ontology, context, or
>> knowledge base.
>>
>> "Unicorn" should not be an individual, since there can be instances in a
>> fantasy world.  Even if the intersection of two classes is empty (e.g.,
>> "square circle"), that intersection should not be an individual even
>> though it has no instances.
>>
>> I note that according to this definition, relations (if they are
>> considered to be entities) are individuals, the application of a relation
>> to a list of arguments, not fitting the definition of "instance" in the
>> definition of "individual".  If a member of a set is not considered to be
>> an "instance" of the set, then sets are individuals.  The same argument
>> applies to "groups" of things -- whose membership can change, unlike sets.
>>
>>> This should help to better characterize the link between ontologies and
>>> individuals.
>> I note that OWL-DL distinguishes "classes" and "instances", as being
>> disjoint.  As such, classes of things (types of wine, animal species,
>> models of car, ...) are often instances in OWL ontologies.  Of course,
>> such things can, themselves, have instances -- even though the
>> impoverished language in which they are represented can not express the
>> relationship between them and their instances as such.
>>
>> Some OWL-DL users use the term "individual" to refer to OWL "instances",
>> even though those instances (in the real world) have instances of their
>> own.  These instances can not have their own instances expressed as such
>> in OWL-DL (although they could be expressed in OWL-FULL).
>>
>>> All the best,
>>> Richard
>>
>>> Le 13/12/2012 16:14, Amanda Vizedom a écrit :
>>>> Hans, et al,
>>>>
>>>> Info Systems might not generally make that distinction, but
>>>> Ontologies, and deployed ontology-based systems can, should, and often
>>>> do.
>>>> The unique name of an individual within an ontology is generally
>>>> artificial, in order to guarantee uniqueness. Namespaces,
>>>> Microtheories, and other mechanisms supporting ontology modularity
>>>> serve to extend that uniqueness beyond the bounds of the original
>>>> ontology or module.  This is quite separate from any identifier used
>>>> for the individual in any other system. Best practice IME is to map to
>>>> identifier systems explicitly, using specific mapping predicates (for
>>>> example, "socialSecurityNumber," "legalName," "vehicleIdentityNumber,"
>>>> "serialNumber," "XYZemployeeID"); those predicates can and should
>>>> themselves be defined with explicit reference to the context in which
>>>> they apply or authority which issues and uses them. Note, also, that
>>>> this approach is essentially neutral to metaphysical questions about
>>>> the individual/class distinction, as identifiers can be, and often
>>>> are, treated as contextual for any thing in the ontology, and mapping
>>>> identifiers for classes is often done in precisely the same way, using
>>>> specific mapping predicates whose context/authority is made explicit
>>>> (for example, "modelNumber," "cHEBIName," etc.).
>>>> This approach also eases things in deployed systems that are used to
>>>> track (and perhaps eventually unify/identify) initially unidentified
>>>> things using partial information.
>>>> Best,
>>>> Amanda
>>>>
>>>> On Thu, Dec 13, 2012 at 9:42 AM, Hans Polzer <hpolzer@xxxxxxxxxxx
>>>> <mailto:hpolzer@xxxxxxxxxxx>> wrote:
>>>>
>>>>
>>>>     MW: Identity is different from identifier...
>>>>
>>>>     HP: Correct! But information systems generally don't make that
>>>>     distinction because the only way they have of distinguishing among
>>>>     individuals is through identifiers -- which have context, usually
>>>>     implicit and overlooked. And one purpose of the "entity primacy"
>>>>     principle is to make developers explicitly aware of that
>>>>     distinction so that they don't mistake the identifiers they are
>>>>     using for individuals for the identity of those individuals (which
>>>>     is their own and inherent in their existence in some reality). The
>>>>     best we can do is to get socio-political agreement on some
>>>>     "near-innate" identifier for individuals, such as VINS for motor
>>>>     vehicles intended for use on public roads and MAC addresses for
>>>>     Ethernet devices. Such identifiers are useful for information
>>>>     sharing interoperability among diverse contexts about the same
>>>>     individuals. But we don't really have such an identifier for
>>>>     people (yet). Maybe some "superDNS" identifier certificate issued
>>>>     independently of national/local jurisdiction before birth to all
>>>>     people (like VINs) will be brought about thanks to the Internet,
>>>>     but I'm not holding my breath. Or maybe some biometric will be
>>>>     found that can serve as this "near-innate" identifier on the
>>>>     network. And we need to be vigilant and remember that even these
>>>>     identifiers are not the same as identity and that the individuals
>>>>     may have other identifiers in other contexts.
>>>>
>>>>
>>>>
>>>>
>>>>
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>>>
>>> --
>>> And the wounded skies above say
>>> it's much too much too late.
>>> Well, maybe we should all be praying for time.
>>>
>>>
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-- 
And the wounded skies above say
it's much too much too late.
Well, maybe we should all be praying for time.    (03)

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