Ontology-Based Semantics

Ciocoiu, Nau

ontology semantics knowledge representation integration translation

@inproceedings{ciocoiu:krr2000,
  title={Ontology-Based Semantics},
  author={Ciocoiu, M. and Nau, D.S.},
  booktitle={International Conference on
             Knowledge Representation and Reasoning},
  pages={539--546},
  year={2000}
}

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With a shared first order language, translation can be formalized as having identical sets of models

With different languages you can't say that

• Different vocabularies, structures, etc., produce different models, even with the same intended semantics

Gruber: Formal ontologies may be used to manage heterogeneity of information from different sources

Different people have different ideas on what constitutes an ontology: Taxonomies, vocabularies with natural text, to formal logic

Systems also vary in commitment to shared ontology: All agents commit, all agents have their own ontologies

This work requires:

• A common ontology capturing all concepts in all agents' ontologies
• A function to convert from sentences of one declarative language to the sentences of the shared first order language
  • Means inputs cannot be strictly more expressive than FOL

Partial translations transfer only subsets of models or consequences

Defines an explanation as a theory including both the interpretation of the logical rendering of the input

A domain theory T \models \Omega, the latter being the ontology

An explanation T is a domain theory such that T \models \Sigma^\pi, the latter being the logical rendering of the input under an interpretation

An ontology-based model is derived from that explanation, obeying the constraints of the ontology

Iff for every model of every explanation of S1, the derived ontology-based model of S1 implies an ontology-based model may be derived for S2, then S2 is an ontology-based partial translation of S1

If that holds in both directions than S1 and S2 are ontology-based translations of each other