## Section: Research Program

### Graph-based Knowledge Representation and Reasoning

Besides logical foundations, we are interested in KR formalisms
that comply, or aim at complying with the following requirements:
to have good *computational* properties and to allow users of
knowledge-based systems to have a maximal *understanding and
control* over each step of the knowledge base building process and
use.

These two requirements are the core motivations for our graph-based approach
to KR.
We view labelled graphs as an *abstract representation*
of knowledge that can be expressed in many KR languages
(different kinds of conceptual graphs â€”historically our main focusâ€” the
Semantic Web language RDF (Resource Description Framework), its extension
RDFS (RDF Schema), expressive rules equivalent to the so-called
tuple-generating-dependencies in databases, some description logics
dedicated
to query answering, etc.). For these languages, reasoning can be based on the
structure of objects, thus based on graph-theoretic notions, while staying
logically founded.

More precisely, our basic objects are labelled graphs (or hypergraphs)
representing entities and relationships between these entities. These graphs
have a natural translation in first-order logic. Our basic reasoning tool is
graph homomorphism. The fundamental property is that graph homomorphism is
sound and complete with respect to logical entailment *i.e.*, given two
(labelled) graphs $G$ and $H$, there is a homomorphism from $G$ to $H$
*if and only if* the formula assigned to $G$ is entailed by the formula
assigned to $H$. In other words, logical reasoning on these graphs can be
performed by graph mechanisms. These knowledge constructs and the associated
reasoning mechanisms can be extended (to represent rules for instance) while
keeping this fundamental correspondence between graphs and logics.