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Upper Ontology Summit March 14, 2006

Upper Ontology Summit March 14, 2006. Michael Gruninger Semantic Technologies Laboratory University of Toronto. Goals. Develop methods to relate the existing upper ontologies to each other. Ontologies reusing an upper level ontology Ontologies sharing an upper level ontology

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Upper Ontology Summit March 14, 2006

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  1. Upper Ontology SummitMarch 14, 2006 Michael Gruninger Semantic Technologies Laboratory University of Toronto

  2. Goals • Develop methods to relate the existing upper ontologies to each other. • Ontologies reusing an upper level ontology • Ontologies sharing an upper level ontology • Create a common subset ontology that is compatible with all of the linked upper ontologies.

  3. Relationships among Ontologies • Theory T1 generalizes theory T2 if and only if T1 is definably interpretable in a theory T3 and T2 is a consistent extension of T3. • Problem: Given two theories T1 and T2, determine whether there exists a nontrivial theory that generalizes both.

  4. Requirements • What do we need so that we can prove that one ontology is a generalization of another? • the ontology must consist of a consistent set of axioms • the ontology must axiomatize its intended models • Evaluation of the relationships between ontologies is made using their axioms alone; it cannot rely on intended models of concepts that are not axiomatized. • If the axioms of an ontology are insufficient to capture their users' intended semantics, then there is little progress that can be made towards integration

  5. Process Specification Language • PSL (ISO 18629) is a modular, extensible ontology capturing concepts required for process specification • There are currently 300 concepts across 50 extensions of a common core theory (PSL-Core), each with a set of first-order axioms written using Common Logic (ISO 24707). • Two kinds of extensions: • Core theories • Definitional extensions

  6. Methodology • Specify class of structures • Existence Theorem • Show that the class of structures is nonempty • Classification Theorem • Characterize the structures up to isomorphism • Satisfiability Theorem • Show that any structure in the class satisfies the axioms of the ontology • Axiomatizability Theorem • Show that any model of the axioms is equivalent to a structure in the class

  7. Modularity and PSL Activity Occurrences Complex Activities Atomic Activities Discrete States Subactivity Occurrence Trees PSL-Core

  8. Definitional Extensions • Preserving semantics is equivalent to preserving models of the axioms. • preserving models = isomorphism • Classify models by using invariants (properties of models that are preserved by isomorphism). • automorphism groups, endomorphism semigroups • Classes of activities and objects are specified using these invariants.

  9. Summary • We have an opportunity to take a rigorous approach to the sharability and reusability of upper level ontologies • This may require extensions or modification of existing ontologies • We can replace the philosophical debates with well-posed logical problems

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