Le 03/01/2013 21:29, Matthew West a écrit :
> Dear John,
>
> See below.
>
>> JFS
>>>> HDQM
>>>> kind_of_activity
>>>> A class_of_activity all of whose members are of the same kind.
>>>>
>>>> Much simpler:
>>>> kind_of_activity: a one-place relation that is true of every
>>>> activity of the same kind.
>> MW
>>> I disagree. Class_of_activity is the supertype of kind_of_activity,
>>> and you leave no place for it. For end users, class is much easier to
>>> relate to than one place relations, which is a logic view point. I
>>> would not with to burden users with that. I might not choose class if
>>> I had my time again, but in ISO 15926 that is history now, and
>>> changing it would be more confusing than leaving it the same.
>> There are four separate issues in that comment:
>>
>> 1. What is the simplest metalanguage for talking about ontology and
>> its mapping to logic?
>>
>> 2. How do you define and explain types and subtypes in ways that are
>> logically sound and pedagogically effective for most people.
>>
>> 3. How do we design a good user interface and explain it to domain
>> experts who have never studied logic or ontology?
>>
>> 4. How are these issues related to specific ISO standards?
>>
>> I answered question #1 in my previous note. The short summary is that
>> all the mainstream logic notations are based on four kinds of primitive
>> notions: relations (or predicates), quantifiers, variables (or names
>> or some graphic equivalent), and Boolean operators. Everything else
>> can be defined in terms of these four.
> MW: If I were wishing to reason over the "ontology" I would probably use an
> ontology language that used those primitives. But that is not the purpose of
> the ontologies I have been developing. The primary purpose has been the
> definition of data structures to hold instance of the ontology, or the
> record structures for the exchange of data. Any reasoning would be over the
> data instances rather than the ontology itself.
>
> MW: There are some interesting requirements that arise from this. You can
> only hold data when you have defined appropriate structures, so much of the
> ontology is permissive, defining the sorts of things that can be said. This
> is not generally the case with logic based ontologies, that are
> unstructured, and when you want to say something you just say it, and you
> are generally not so concerned with instances of the ontology (though you
> can be of course, but it is likely to be rather inefficient if there are
> large volumes of instances).
> The result of this is that much of the ontology is permissive, setting out
> the kinds of things that can be said. Logic is not particularly good for
> this, but an entity relationship language such as EXPRESS is. It has the
> things that you describe. So for example, in the definition you took an
> excerpt from:
>
> ENTITY class_of_spatio_temporal_extent
> SUBTYPE OF (class);
> member_of_ : OPTIONAL SET [1:?] OF
> class_of_class_of_spatio_temporal_extent;
> END ENTITY;
>
> The first line says that class_of_spatio_temporal_extent is an ENTITY (this
> is equivalent to saying that class_of_spatio_temporal_extent is a unary
> predicate)
>
> The second line says that class_of_spatio_temporal_extent is a subtype of
> class.
>
> The third line (a bit turtle like) declares a binary predicate where the
> places are filled by a member of class_of_spatio_temporal_extent and
> class_of_class_of_spatio_temporal_extent.
>
> You have of course picked just about the most obscure bit of the data model,
> but instances of class_of_spatio_temporal_extent are the subtypes of
> spatio_temporal_extent, and instances of
> class_of_class_of_spatio_temporal_extent are subtypes of
> class_of_spatio_temporal_extent. These are structures you need to give
> yourself flexibility and extensibility at lower levels. If you don't make
> these declarations, you can't hold those things.
Dear Matthew,
I see that what you define here seems to meet our purposes, however the
means are different.
The works we are developing for certified ontologies use instead a
higher order (dependent) type theoretic approach (based on
intuitionistic logic) which associates types and logic for representing
concepts (type), relations (type) and specifications (logic), at
different abstraction levels.
Specifications are pairs where the left term is either a concept or a
relation, and the right term a predicate expressing axioms that the
respective concepts or relations must satisfy. (01)
The logic we have used allows for the expressive definition of dependent
sum types (type classes in Coq) along with the definition of instances.
In such a way, we represent concepts with dependent sum types that are
expressed inside the logic.
Type classes (Coq implementation) can be parameterized (parameters
transmitted as function arguments) and support inheritance (coercive
subtyping). Not only we can reason over the "ontology", but we can
compute instances (for types) or proofs (for predicates) and check if
these instances and proofs are valid w.r.t. their type definitions.
Best,
Richard
>> Aristotle answered question #2 in a form that is widely used today:
>> assign a noun phrase to each category (monadic relation) in ontology.
>> In the 3rd century AD, Porphyry organized the categories in a tree and
>> introduced the drawing conventions we still use today.
> MW: That is pretty much what we do, and EXPRESS-G gives you a reasonable
> graphical form for the tree (there is multiple inheritance of course).
>> For question #3, my recommendation is to develop tools that use the
>> same terminology and diagrams that the domain experts use. That means
>> that we need tools that can support controlled NLs and widely used
>> graphics.
>> The tools should support methods for tailoring the graphics by adapting
>> symbols, shapes, and styles to the conventions of any special domain.
> MW: There is a big gap between what domain experts do and what is necessary
> for ontology. Generally ontology requires greater precision than is usually
> provided by domain experts without specific training. The alternative is to
> have an intermediary who does the analysis to fill the gap between the
> domain experts and the precision needs of an ontology.
>> For question #4, we cannot change any official standard. But we can
>> recommend mappings of the standards to and from the notations above.
> MW: Indeed. The EXPRESS version of ISO 15926 has already been mapped to OWL
> full. Generally, you cannot perform an automated mapping, you rather have to
> do a restatement in terms of the new language, taking account of its
> particular limitations and capabilities.
>
> Regards
>
> Matthew West
> Information Junction
> Tel: +44 1489 880185
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> Skype: dr.matthew.west
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