Re: [ontolog-forum] Is there something I missed?

[Ali Hashemi <ali.hashemi+ontolog@xxxxxxxxxxx>]

I don't mean to say that there ought not be a taxonomy or a hierarchy; rather that perhaps too much is energy and attention has been focused on that component of ontologies and particularly, they shine when they are seen as being much more than that. 

Much (if not most) of the semantics of an ontology is contained in the axioms, not the hierarchy.

Pat Hayes wrote:
> In practice, there seems to far more unary/binary than anything else,
> and one can routinely encode an n-ary relation is a conjunction of
> binary ones. 

While true, it seems to create an odd barrier to more natural expressions of an idea. In my mind, such a perspective unduly emphasizes and elevates dyadic and monadic relations, which can affect how a problem or situation is perceived, especially when familiarity with the language of representation is perhaps only a touch more than cursory.

/Ali

On Thu, Jan 29, 2009 at 11:57 AM, Pat Hayes <phayes@xxxxxxx> wrote:

On Jan 29, 2009, at 9:14 AM, Ali Hashemi wrote:

The following from Guarino (2008) is apt here, i think:

In the philosophical sense, we may refer to an ontology as a particular system of categories accounting for a certain vision of the world. As such, this system does not depend on a particular language: Aristotle's ontology is always the same, independently of the language used to describe it. On the other hand, in its most prevalent use in AI, an ontology refers to an engineering artifact, constituted by a specific vocabulary used to describe a certain reality, plus a set of explicit assumptions regarding the intended meaning of the vocabulary words. This set of assumptions has usually the form of a first-order logical theory, where vocabulary words appear as unary or binary predicate names, respectively called concepts and relations. In the simplest case, an ontology describe a hierarchy of concepts related by subsumptions relationships; in more sophisticated cases, suitable axioms are added in order to express other relationships between concepts and to constrain their intended interpretation.

(Guarino 2008, pp14-15)

Though i'm not sure why vocabulary words are restricted to unary or binary predicate names

Me neither. Writing in 2008, Nicola was probably intending to make a nod at the prevailing widespread use of description logics, which are restricted to the unary/binary case. 

, it seems there'd be a lot of useful things to say with terms that range directly over n variables.

An observation on a lot of literature i've come across, a lot seems to focus on the taxonomic component of ontologies, when they can be, as Guarino notes, more sophisticated. I wonder if this might be a reason there have been no killer apps for the field yet.

Most ontologies are built on a skeleton of taxonomy, or at least a subclass hierarchy. Its hard to avoid having such a structure somewhere in any large ontology, in fact. NOt sure if this amounts to a criticism, though.

PatH

// Ali

On Thu, Jan 29, 2009 at 9:33 AM, Pat Hayes <phayes@xxxxxxx> wrote:

On Jan 29, 2009, at 5:55 AM, Azamat wrote:

> On Thursday, January 29, 2009 1:15 AM, Sean aked:
> "is there a formal definition of an ontology?"
>
> Good question.  It seems there are as many definitions as many
> schools,
> researchers and developers.
> But the right one is that involving the original nature and meaning of
> ontology as:
> "Formal Ontology is the formal study of Reality".

That is the definition of ontology, the philosophical field. When the
word is used in this (original) sense, the construction "an ontology"
is ungrammatical. The sense of "ontology" agreed to in this forum
dates back less than two decades, and has its origin in AI, not
philosophy. While the two senses are related, its important not to get
them confused with one another.

PatH

> The issue of issues is how
> Reality is related with the whole world (the totality of entities and
> relations), particular worlds, or possible worlds; and how it could
> be truly
> and consistently represented and effectively reasoned [by humans and
> machines].
>
> Azamat Abdoullaev
> http://www.eis.com.cy
>
>
> ----- Original Message -----
> From: "Sean Barker" <sean.barker@xxxxxxxxxxxxx>
> To: <ontolog-forum@xxxxxxxxxxxxxxxx>
> Sent: Thursday, January 29, 2009 1:15 AM
> Subject: [ontolog-forum] Is there something I missed?
>
>
>>
>>
>> Folks
>>
>> Having followed this forum for some time, I have a feeling that I
>> may have
>> missed something so obvious that no-one has thought to mention it -
>> that
>> is,
>> is there a formal definition of an ontology? An ontology cannot be
>> just be
>> a
>> bowl of axiom soup, so how does one tell that a particular
>> collection of
>> axioms is an ontology - the question is posed on the analogy that
>> mathematicians differentiate between a group, a ring and a field by
>> the
>> axioms they include. My naive guess for this would be based on set
>> theory,
>> and look something like:
>>
>> 1) A set S can be defined as S = {x s.t. x satisfies some
>> combination of
>> predicates};
>> 2) Given a set of predicicates P = {p1, p2,...,pn} and a set of
>> logical
>> operaters L = {l1, l2,...,ln} (perhaps just AND, OR and NOT), then
>> denote
>> Spl as a set defined from some combination of predicates in P and
>> operators
>> in L, and Spl* is the set of all possible sets Spl (perhaps
>> regularised to
>> remove contraditions);
>> 3) An ontology is constructed by taking a collection of sets from
>> Spl* and
>> identifying a partial ordering of those sets using the usual subset
>> relationship.
>>
>> This would split the study of ontology into three area:
>> 1) the formal problem of ontology as being concerned with the types
>> of
>> mappings (homomorphisms, homeomorphisms, etc) between different
>> ontologies
>> based on the choices from some Spl*
>> 2)the practical problem as finding an ontology that supports the
>> decision
>> procedures in a particular process (I include classifying something
>> as a
>> decision procedure).
>> 3) the computational problem of defining of terminating and efficient
>> procedures for comparing ontologies and mapping between them.
>> (Thanks to Pat Hayes for this suggestion - even his more acerbic
>> comments
>> can be quite enlightening.)
>>
>> I would then expect there to have been a number of competing
>> definitions,
>> and any number of arguements discussing the relative merits of these
>> definitions. And possibly some argument demostrating that this whole
>> approach is flawed.
>>
>> My question is, where are these definitions and the ensuing
>> arguments? and
>> is there a good summary of these?
>>
>> Sean Barker
>> Bristol, UK
>>
>>
>>
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