|From:||William Frank <williamf.frank@xxxxxxxxx>|
|Date:||Mon, 24 Feb 2014 13:58:36 -0500|
On Mon, Feb 24, 2014 at 8:05 AM, John F Sowa <sowa@xxxxxxxxxxx> wrote:
On 2/23/2014 11:18 PM, William Frank wrote:
(by the way, I wrote this before receiving Ed's remarks on the subject. I have to agree with him that 0-ary 'relations' are problematic, and worthy of more consideration. As an overview, I think the computer science side of the problem can be approached with the iota operator and the lamda operator, while I would fully expect that my philosophical ontology is naive, and fraught with potential contradictions.
I have no objection to using terms like 'entity', 'attribute',
Exactly. In other words, they are DERIVED terms.
For example, my preferred axiom for entity:
Exactly. That reification hagling was the very most convoluted part of the dasterdly official UML semantics. They actually believed that each 'level' of abstraction was a model of **a different world**, hence metametameta models. I thought this went out in logic with Carnap, almost 75 years ago. Now, logicians use 'meta' the way you do below. As a way to discourse about the language of some other discourse, E.g. a meta model for ontologies) not as of 1930's-old and of the (bad) 'fathers of UML" where they seem to use it as a way to separate sets from individuals, sets of sets from sets, etc, and treat them all as somehow incompatable.
Your set of axioms here is exactly what I have been using implicitly. The roles in a relation are yet more entities, of course.
I only just now rediscovered, following along the Fillmore path, that the idea of 'case grammars', which after all, are syntactic features of individual langauges, has been largely replaced in generative linguistics by the concept of a 'theta role', an underlying set of trans-language roles that enable inter-language mappings.
As far as I know, this began with Ed Keenan's discovery of what he at-the-time called 'voices' in Malagasy, where the subject of a sentence is preceded by a separate particle that describes in role in the verb. A more formal and modern presentation of this is in his "Morphology is Structure - A Malagasy Test Case"
A class is defined as a pair (t,s), where t is a monadic relation
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