Section: Overall Objectives
Logic and Graph-based KRR
The main research domain of GraphIK is Knowledge Representation and Reasoning (KRR), which studies paradigms and formalisms for representing knowledge and reasoning on these representations. We follow a logic-oriented approach of this domain: the different kinds of knowledge have a logical semantics and reasoning mechanisms correspond to inferences in this logic. However, in the field of logic-based KRR, we distinguish ourselves by using graphs and hypergraphs (in the graph-theoretic sense) as basic objects. 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 graph-theoretic notions), with homomorphism as a core notion, while being sound and complete with respect to entailment in the associated logical fragments. An important issue is to study trade-offs between the expressivity of languages and the computational tractability of (sound and complete) reasoning in these languages.