Re: [ontolog-forum] Axiomatic ontology
Wednesday, January 30, 2008 1:10 AM, Avril wrote:
> We have to separate two things:
>
> 1) formalization
> 2) axiomatization
That's correct. There are formal ontologies and axiomatic ontologies. The
common meaning is that both deal with the elements common to all sciences,
but in two different ways, formal or scientific. The former overexploits
formal conceptual tools as formal logic, set theory, category theory,
dissolving in the formal schemes, like the sugar in the coffer, leaving
aside real significance. The latter employs both mathematics and science
concentrating on the content and the matter of things, zooming in on real
meanings. A genuine computing ontology is real, axiomatic, and formal.
For instance, if one constructs the time ontology, just giving formal
logical description of the relationships in time (as after, before, at,
during, in, on, from, to; period, time unit, interval, moment, and instant)
is not enough. This is better done by natural language. In real time
ontology, one needs to build an axiomatic theory of time by formulating a
body of primitve concepts and true statements (definitions, axioms, and
rules). What requests to specify the following:
1. what class of things the time might belongs, a self-existing entity
containing all things or a sort of relationships among things:
2. does it exists or not (is it a reality or illusion ?);
3. how it exists (a reality, a concept, an illusion, an experience of
change, a quantity, a motion, a clock);
4. what are its kinds and parts (the past, the present now, the future; an
instant, moment, unit, interval, period);
5. how it relates to space, change and causality.
6. how it relates to human mind.
7. what is it's reference states and measure (a potential clock, time unit
or unit of time), etc.
For, by its essential nature and meaning, time is a special type of
relationship, infinite duration or limitless succession, while our common
time is measured (or measurable) duration of some process, change, event,
action, or state: ''number of motion in respect of the before and after. So,
without process ontology, no time ontology; since no changing things, no
time, no temporal intervals, nor temporal seperation between different
states or actions. [ as sample, see Bunge's formal ontology of time].
Sum up: The difference between formalization and axiomatization is worth of
great care to avoid false formal ontologies; besides, still many
applications developers hold the idea that ontological engineering has
something to do with formal logical systems.
Azamat