SUO: RE: free logics, unary relations and the entity classification
Dear Robert,
As someone who come from a background of databases rather than logic
and AI, I sometimes feel I have arrived on another planet, so let me
try to state my position on some of the matters you raise (and others
have raised in response to you).
1. By free logic I presume you mean a logic with only free variables
(which I gather would be equivalent to a logic with universal variables).
2. I have never been able to distinguish a difference between a predicate
and a class (taking class as the broadest kind of thing that has members).
Being a predicate only seems to me to be to do with the role the class
plays in a particular statement. KIF seems to allow this view. I would
not particularly want to impose this view on others, i.e. it is OK with
me to allow that there are two classes, one of which is a predicate and
one of which isn't, and they have the same members, but equally I would
object to having to have both a class and a predicate and say they were
the same.
3. At the level of class I am talking about, such things as sorts, types,
attributes, properties, and sets would all be included. All would be defined
extensionally. Again, I don't mind that others want more than one class with
the same extension, but I want simply to be able to deal only with
extensionally
unique classes. The distinctions many would want to see are about the
common properties of sets of classes (e.g. non-overlapping tree structure).
I would want to be able to specify these meta-level properties all within
the one space.
I hope some of this is relevant.
Matthew West
Principal Consultant
Shell Information Technology International Limited
Shell Centre, London SE1 7NA, United Kingdom
Tel: +44 20 7934 4490 Other Tel: +44 7796 336538
Email: matthew.r.west@is.shell.com
Internet: http://www.shell.com
> -----Original Message-----
> From: Robert E. Kent [mailto:rekent@ontologos.org]
> Sent: 16 July 2002 23:55
> To: SUO
> Subject: SUO: free logics, unary relations and the entity
> classification
>
>
>
> All,
>
> I have been thinking about free logics in the IFF recently.
> Recall that an
> IFF model offers an interpretative semantics, an IFF theory
> offers a formal
> or axiomatic semantics, and an IFF logic offers a combined
> semantics, since
> it incorporates the notions of an IFF theory and an IFF
> model. Every logic
> has an underlying theory -- just forget the model-theoretic
> aspect. This
> defines a theory passage from the logic context to the theory
> context in the
> IFF. A free logic over an IFF theory adds an IFF
> model-theoretic structure
> (entity and relation classifications) in a certain universal
> (free) fashion.
> Intuitively, freeness would add an interpretative semantics
> to a formal
> semantics in a nicely compatible fashion. More technically,
> the notion of a
> free logic would define a logic passage (in the opposite
> direction of the
> theory passage) from the theory context to the logic context
> in the IFF, and
> this logic passage would be a generalized inverse to the
> theory passage.
>
> In my thinking about the notion of a free IFF logic the
> following issue has
> come up. It has surfaced before, but not in such a strong
> fashion. In the
> notion of an IFF model (aka model-theoretic structure, model or
> interpretation) there are both unary relation types and
> entity types, and
> these are connected by the constraint that for any unary
> relation type R
> whose signature (sort) is the one-tuple (E) for some entity
> type E, any
> one-tuple r where r |=rel R must have a signature (e) for some entity
> instance e where e |=ent E. Put in more colloquial terms, if
> e satisfies the
> unary relation R, r = R(e) holds, then e is of type (sort) E.
> Should this
> constraint be stronger? Should it be an equivalence? In fact, could we
> identify unary relation types (unary predicates) with entity
> types (sorts)?
> What are the advantages for doing this?
>
> The IFF Model Theory Ontology (IFF-MT) has a lax notion of
> satisfaction for
> tuples. If a tuple r satisfies a relation type R, we only
> require that the
> arity of R be a subset of the arity of r, and that the
> restriction of r to
> that subset satisfy R in the usual sense. When free logics
> are investigated
> with respect to this lax notion of satisfaction, then the
> equivalence or
> identification of unary relation types with entity types looks very
> attractive. So my question to you all is: does anyone have any
> philosophical, theological, linguistic, political, or artistic, etc.
> objections to the identification of unary relation types with
> entity types?
>
> Robert E. Kent
> rekent@ontologos.org
>
>
>
>
>
>
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>