Ontology-Based Semantics

We consider the problem of providing semantics for declarative languages, in a way that would be useful for enabling automated knowledge exchange. If we only have one (first order) language, we can formalize what we mean for a set of sentences to be a translation of another, by requiring that the two sets share the same models. However, in order to formalize translation for the case where the two sets of sentences are of different languages, we need a different notion of semantics, capable of overcoming the language barrier. We introduce Ontology-Based Semantics with this purpose in mind. We show how ontologies can be used to make implicit assumptions explicit, and how they are integrated in our semantics in order to restrict the set of models a set of sentences has. We show how Ontology-Based Models can be used to formally define knowledge translation for the different language case in a similar way ordinary models can be used to define translation for the one language situation. We also provide a syntactical characterization of knowledge translation, that can be used as an effective procedure to check translatability, and we prove it to be sound and complete with respect to our semantic definition of translation.