## Section: Scientific Foundations

### Graph-based Knowledge Representation and Reasoning

Besides logical foundations, we are interested in KRR 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 specific
approach to KRR, which is based on labelled *graphs*.
Indeed, we view labelled graphs as an *abstract representation*
of knowledge that can be expressed in many KRR languages
(different kinds of conceptual graphs —historically our
main focus—, the Semantic Web language RDFS,
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 on
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 reasonings 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.