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On Wed, Jan 21, 2009 at 5:28 PM, Pat Hayes <phayes@xxxxxxx> wrote:
Any set of axioms has with it an associated set of models. These set of models are extensions of the relations, functions etc. of the axiom. Let's say some binary relation Rb has an extension of = {<a,b> , <c,d> ... } In general, the extension corresponds to elements from the domain of the axiom set - i.e. in PSL the subactivity relation ranges over activities. The acceptable models of subactivity will consist of pairs of activities. If we take a step back and denude this extension from the particular domain and instead look at it as a model with abstract symbols populating the extension, we find that the models of subactivity are in fact isomorphic to the models of a join semi distributive lattice (JSDL). It is in this sense that we are "reusing the model theoretic structures." We don't necessarily want to reuse the concept of JSDL, but we are nevertheless reusing its models. That's what i mean. Those ontologies of time you cataloged, "map into" / "reuse" various subclasses of partial orders. /// other tangent: [Pat Hayes] 5. There is a meaningful relationship of being more primitive than, which holds between concepts in a (large enough) ontology (C, ~H) [/end] Would an ordering of theories by representation theorems make sense? i.e. you define a "base" set of FOL theories (layer 10. You show that other theories (layer 2) "map" into them by representation theorems. You might also show that say a 3rd layer map into the 2nd by representation theorems, now being rank 2 away from the layer 1. See attached diagram for a possible design. I can think of at least two ways to define the red lines in that diagram, one of them being explicated in this email -- representation theorems. //ali
-- (•`'·.¸(`'·.¸(•)¸.·'´)¸.·'´•) .,.,
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