South American Journal of Logic 3 (2):517-531 (2017)

Jens Lemanski
Fernuniversität Hagen
The paper presents the diagrammatic calculus CL, which combines features of tree, Euler-type, Venn-type diagrams and squares of opposition. In its basic form, `CL' (= Cubus Logicus) organizes terms in the form of a square or cube. By applying the arrows of the square of opposition to CL, judgments and inferences can be displayed. Thus CL offers on the one hand an intuitive method to display ontologies and on the other hand a diagrammatic tool to check inferences. The paper focuses mainly on the adaptation of the square of opposition in CL and offers an algebraic notation, which corresponds to the diagrammatic representation.
Keywords logic  Calculus CL  square of opposition  oppositional geometry  universal logic  ontology engineering
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