Concept Graphs without Negations: Standard Models and Standard Graphs

In this article, we provide different possibilities for doing reasoning on simple concept(ual) graphs without negations or nestings. First of all, we have on the graphs the usual semantical entailment relation ⊧, and we consider the restriction ⊢ of the calculus for concept graph with cuts, which has been introduced in [Da02], to the system of concept graphs without cuts. Secondly, we introduce a semantical entailment relation ⊧ as well as syntactical transformation rules ⊢ between models. Finally, we provide definitions for standard graphs and standard models so that we translate graphs to models and vice versa. Together with the relations ⊧ and ⊢ on the graphs and on the models, we show that both calculi are adequate and that reasoning can be carried over from graphs to models and vice versa.