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## Section: Research Program

### Knowledge representation semantics

We work with semantically defined knowledge representation languages (like description logics, conceptual graphs and object-based languages). Their semantics is usually defined within model theory initially developed for logics.

We consider a language $L$ as a set of syntactically defined expressions (often inductively defined by applying constructors over other expressions). A representation ($o\subseteq L$) is a set of such expressions. It may also be called an ontology. An interpretation function ($I$) is inductively defined over the structure of the language to a structure called the domain of interpretation ($D$). This expresses the construction of the “meaning” of an expression in function of its components. A formula is satisfied by an interpretation if it fulfills a condition (in general being interpreted over a particular subset of the domain). A model of a set of expressions is an interpretation satisfying all the expressions. A set of expressions is said consistent if it has at least one model, inconsistent otherwise. An expression ($\delta$) is then a consequence of a set of expressions ($o$) if it is satisfied by all of their models (noted $o\vDash \delta$).

The languages dedicated to the semantic web (rdf and owl ) follow that approach. rdf is a knowledge representation language dedicated to the description of resources; owl is designed for expressing ontologies: it describes concepts and relations that can be used within rdf .

A computer must determine if a particular expression (taken as a query, for instance) is the consequence of a set of axioms (a knowledge base). For that purpose, it uses programs, called provers, that can be based on the processing of a set of inference rules, on the construction of models or on procedural programming. These programs are able to deduce theorems (noted $o⊢\delta$). They are said to be sound if they only find theorems which are indeed consequences and to be complete if they find all the consequences as theorems.