Defeasible Mappings.pdf

The authors propose a novel approach to denote mappings between EL-based ontologies, which are defeasible in the sense that such a mapping only applies to individuals if it does not cause an inconsistency. This approach provides the advantage of handling exceptions automatically and avoiding logical inconsistencies that may be caused due to traditional type mappings.

The authors consider the case where mappings from many possibly heterogeneous ontologies are one-way links towards an overarching ontology, allowing questions to be asked in terms of the concepts in the overarching ontology. They provide formal semantics for the defeasible mappings and show that reasoning under such a setting is decidable, even when the defeasible axioms apply to unknowns.

The proposed language, ER⊥,O, allows for conjunction, existentials, role chains, disjointness of concepts, and ABox statements. The authors define the semantics along similar lines to default logic and show that combining DLs with default-like semantics is not straightforward, as unrestricted default applications may result in undecidability.

The authors demonstrate the decidability of their approach, which results from the restriction to a tractable language in the EL family and the avoidance of recursion through the defeasible axioms. They also show that the semantics of their approach is strongly related to the idea of answer sets for logic programs.

The paper provides a formal framework for dealing with defeasible reasoning for smaller fragments of DLs, especially in the context of ontology alignment. The authors discuss the motivation for using defeasible axioms as alignments, stemming from the need to handle heterogeneity among various data models. They also provide an example illustrating the benefits of using defeasible axioms in ontology alignment.

Key points:

Defeasible mappings between EL-based ontologies are proposed to handle exceptions automatically and avoid logical inconsistencies.
The authors consider one-way links towards an overarching ontology, allowing questions to be asked in terms of the concepts in the overarching ontology.
Formal semantics for the defeasible mappings are provided, and decidability is shown, even when the defeasible axioms apply to unknowns.
The proposed language, ER⊥,O, allows for conjunction, existentials, role chains, disjointness of concepts, and ABox statements.
The approach is decidable due to the restriction to a tractable language in the EL family and the avoidance of recursion through the defeasible axioms.
The semantics of the approach is strongly related to the idea of answer sets for logic programs.