Logic Graphs: A complete visualization method for logical languages based on Ch. S. Peirce’s existential graphs Dmitry Mouromtsev and Ildar Baimuratov ITMO University, 49 Kronverksky Pr., 197101 St. Petersburg, Russia d.muromtsev@gmail.com, baimuratov.i@gmail.com Abstract. Contemporary tools of graph data visualization do not allow to work with logic expressions completely. The purpose of our research is to develop a complete and convenient method for its visualization. The developed prototype is intended for realization in the Ontodia library. We analyze the tools of Ontodia with respect to description logic syntax and adopt required tools from Ch. S. Pierce’s existential graphs system. In addition, we propose to use schemes of expression for prompting to a user, optimizing data structure and explicating an ontology structure. We illustrate the developed method, named logic graphs, on a simple demo-ontology. Keywords: Visualization · Description Logic · Existential graphs. 1 Introduction The purpose of our research is to develop a complete and convenient method for logic expressions visualization. Contemporary tools of graph data visualiza- tion do not allow to work with logic expressions completely, while necessity to work with them in visual format is obvious. Providing to a user an opportunity to observe ontologies constructed by axioms would be extremely useful. The developed prototype should be suitable for realization in the Ontodia library [1]. 2 Tools overview We present an overview of the existing ontology visualization tools. VOWL. In the current realization of VOWL [2] it is impossible to represent a composition of two and more logic operators. For example, consider an axiom W oman ≡ P erson ⊓¬Man (1) which means “A woman is a person, who is not a man”. Its visualization is given at the Fig. 1. In this axiom the negation of the concept Man is also a part of conjunction, while at the visualization only the negation is represented. Besides, VOWL language is not satisfactory, as logic relations are not visualized, but only symbolically depicted, this in substance does not differ from a formula.