# Model-Theoretic Approaches to Semantic Integration

## Gruninger

` model theory semantic translation invariant interlingua psl is2010q1 `

@inproceedings{gruninger:dsp-2005,
author={Michael Gr{\"u}ninger},
title={Model-Theoretic Approaches to Semantic Integration},
booktitle={Semantic Interoperability and Integration},
year={2005},
series={Dagstuhl Seminar Proceedings},
number={04391},
publisher={Internationales Begegnungs- und Forschungszentrum
f{\"u}r Informatik (IBFI), Schloss Dagstuhl, Germany},
editor={Y. Kalfoglou and M. Schorlemmer and A. Sheth
and S. Staab and M. Uschold},
url={\url{http://drops.dagstuhl.de/opus/volltexte/2005/39}},
}

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"A semantics-preserving exchange of information between two software applications requires mappings between logically equivalent concepts in the ontology of each application."

- Semantic integration is then generating mappings, verifying, and executing

Current approaches: Based on taxonomic structure, heuristics-based comparisons of the symbols

To automate, prove correct, need stronger, model theoretic techniques

PSL has core ontology, definitional extensions providing richer lexicon

- Extensions based on invariants, properties preserved by isomorphism, that partition models of the core ontology

Several definitions needed to define translation

"Considering interoperability among complete first-order inference engines that exchange first-order sentences"

- First order to maintain completeness
- Complete reasoners required in order to ensure it's not possible to exchange sentences that have models falling within the recipients ontology, but which cannot be derived

Examples of structures

- Graphs, linear orderings, partial orderings, groups, fields, vector spaces

"Ontological Stance: Given an application $A$, there exists a class of models $M^A$ such that any sentence $\Phi$ is decided by $A$ to be satisfiable iff there exists $M \in M^A$ such that $M \models \Phi$."

- Even if the application does not use an explicit ontology, we can still treat it as such

Definitional extensions based around invariants of core models

- Helps identify coverage
- Makes it easier to characterize application
- Bootstrap application ontologies