Background Knowledge in Concept Graphs

Traditional logic can be understood as the investigation of the three main essential functions of thinking – concepts, judgements and conclusions. In the last years, in a new research field termed Contextual Logic, a mathematical theory of this logic is elaborated. Concepts have already been mathematically elaborated by Formal Concept Analysis. Judgements and Conclusions can be expressed by so-called Concept Graphs, which are built upon families of formal contexts. There are two approaches to concept graphs: A semantical approach, which investigates the theory of concept graphs in an algebraic manner, and a logical approach, which focuses on derivation rules for concept graphs, relying on a separation between syntax and semantics. In [26], Wille introduced two forms of complex implications (object implications and concept implications) to the semantical approach. In this paper it is investigated how these implications can be incorporated into the logical approach.