Preservation of Modules

Within the Common Logic Ontology Repository (COLORE), relationships among ontologies such as the notions of faithful interpretability, logical synonymy, and reducibility have been used for ontology verification. Earlier work has shown how to use these relationships to find modules of theories, so a natural question is to determine how we can use the decomposition of one theory into modules to find the modules of another theory in the repository. In this paper, we examine a number of ontologies for which faithful interpretability and logical synonymy do not preserve their modules. Nevertheless, we identify a class of interpretations among theories which guarantees that the modules of a theory are preserved. We also show that the modules of reducible theories are preserved by logical synonymy.

[1]  CHARLES C. PINTER,et al.  Properties Preserved under Definitional Equivalence and Interpretations , 1978, Math. Log. Q..

[2]  Herbert B. Enderton,et al.  A mathematical introduction to logic , 1972 .

[3]  Johan van Benthem,et al.  The logic of time - a model-theoretic investigation into the varieties of temporal ontology and temporal discourse, 2nd Edition , 1982, Synthese library.

[4]  Sergiu Rudeanu,et al.  Axioms For Lattices And Boolean Algebras , 2008 .

[5]  Chiara Del Vescovo,et al.  The Modular Structure of an Ontology: Atomic Decomposition , 2011, IJCAI.

[6]  David Pearce,et al.  Synonymous theories and knowledge representations in answer set programming , 2012, Journal of computer and system sciences (Print).

[7]  Boris Konev,et al.  Formal Properties of Modularisation , 2009, Modular Ontologies.

[8]  Patrick J. Hayes,et al.  A Catalog of Temporal Theories , 2005 .

[9]  Paulo A. S. Veloso,et al.  On conservative and expansive extensions , 1991 .

[10]  Michael Grüninger,et al.  Verification of Time Ontologies with Points and Intervals , 2011, 2011 Eighteenth International Symposium on Temporal Representation and Reasoning.

[11]  Torsten Hahmann,et al.  Modular first-order ontologies via repositories , 2012, Appl. Ontology.

[12]  L. W. Szczerba,et al.  Interpretability of Elementary Theories , 1977 .

[13]  Ian Horrocks,et al.  Extracting Modules from Ontologies: A Logic-based Approach , 2009, OWLED.

[14]  Stefano Spaccapietra,et al.  Modular Ontologies: Concepts, Theories and Techniques for Knowledge Modularization , 2009, Modular Ontologies.