On the Visualization of Logic: A Diagrammatic Language Based on Spatial, Graphical and Symbolic Notations

摘要

Visual languages are studied in many different disciplines including Formal Logic. Several diagram methods have been proposed for the visual representation of the logical relations and in particular for First Order Predicate Logic (FOPL) formulas. Among these, logical symbolism, Euler diagrams, semantic networks, conceptual grids, conceptual spaces and so on. It is shown that these representations are formally equivalent and can be inter-translated algorithmically, but provide different and complementary visualizations such that the use of multiple representations may provide greater insight than any alone. We present a new visual language, V-Logic, which support different visual representation schemes: spatial, graphical and symbolic notations. It specifies rules for mapping FOPL formulas in special semantically equivalent diagrams, named V-diagrams. Logical inference based on the interpretation of a V-diagram is essentially a translation of the diagram into a logical formalism. Such a translation is natural and could be used to teach FOPL. We performed a preliminary study with 10 students. Results provided us with overall positive feedback about the effectiveness of our approach as well as further directions to explore.