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**Thursday, December 15, 2005**

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**Communications on lattice of theories and**

**conceptual atomism**

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Given our historical background; and John Sowa’s work on a (substructural) framework that has 12 primitives, it is possible to make a formal linkage between deep notions on lattice of formal constructions (ie models or theories) and some type of aggregation process that helps identify the proper formal construction for a specific situation (or web service)?

Sowa’s note on mapping language games to formal complexes begins to lay this out.

How can a specification of formal linkage start?

Perhaps with a full development of what Sowa’s Unified Framework concept is?

John

Is there an appropriate “smallest” ontological construction? Is this the Unified Framework?

Can a smallest ontological construction be specified as a set of concepts with properties, relationships, attributes and facets? Can this conceptual specification occur without the introduction of predicate logic? After conceptual specification, can the predicate logic be used to create a standard OWL construction with these concepts?

Can we count the concepts, properties, relationships, attributes and facets?

What part of Suggested Upper Merged Ontology (SUMO) has a one to one mapping to the smallest ontological construction (SOC ? ). Do the other upper, common, or abstract ontologies have one to one mappings to the smallest ontological construction?

(Now, I agree that this might not work out. But I am willing to try to push forward the formalism and grounding theory.)

Perhaps this might work, if it starts should be off - line?

Is there principled criticism of our spending a few weeks talking about this?

Paul Prueitt

The ** Entscheidungsproblem**
(English: decision
problem) is the challenge in symbolic
logic to find a general algorithm which decides for given first-order statements whether they
are universally valid or not. In 1936, working independently, Alonzo
Church and Alan Turing both showed that this is impossible. As a
consequence, it is in particular impossible to algorithmically decide whether
statements in arithmetic are true or false.

From http://en.wikipedia.org/wiki/Entscheidungsproblem

Combinatory
logic was intended as a simple 'pre-logic' which would clarify the meaning of
variables in logical notation, and indeed eliminate the need for them.