Presenting Proofs Using Logicographic Symbols ? Koji Nakagawa, Bruno Buchberger Software Competence Center Hagenberg, Hauptstrasse 99, A-4232 Hagenberg, Austria koji.nakagawa@scch.at Research Institute for Symbolic Computation, Johannes Kepler University, A-4040 Linz, Austria {nakagawa, buchberger}@risc.uni-linz.ac.at Abstract. Mathematics has a rich tradition in creating symbols and notation that is soundly integrated into the syntax of the underlying formal language and, at the same time, conveys the intuition behind the concepts described by the symbols and notation. Continuing this idea, in the Theorema system, with the new feature of logicographic symbols, we now provide a means to invent arbitrary new symbols and notation. In this paper we describe how logicographic symbols can be created, declared, and afterwards used as a part of the formal language of The- orema with an example. Also with logicographic symbols, formal proof text automatically generated by Theorema provers can become easy to read in a way that resembles telling a pictorial story about the mathe- matical concepts involved. 1 Introduction In automated theorem provers, it is very important not only to produce formal proofs but also present proofs that can be easily understood by humans, see [1, 2]. One of the issues in facilitating human understanding of automatically generated proofs is the automated generation of natural language explanatory text as part of the proofs, see for example [3, 4]. Also, in the Theorema system[5, 6], an coherent mathematical environment for proving, solving, and computing implemented on top of M athematica[7], we put a lot of emphasis on the natural language aspect of proof presentation. This is achieved by, first, using natural deduction calculi with special complex inference rules for the various special areas of mathematics and, second, by producing standardized natural language text blocks that are produced, in a post-processing step, with every application of these inference rules. In this paper we describe a new and additional feature of the Theorema sys- tem, first proposed in [8], that should improve the readability of formal texts, in ? Work on this paper was supported by Project MathSoft of the Software Competence Center Hagenberg (Austria) and Project F1302 of the Austrian Science Foundation (FWF). We would like to thank Christopher Carlson and Theodore W. Gray of Wolfram Research Inc. for their aid and valuable advice on subtle details of the M athematica front end.