Explaining Modal Logic Proofs

There has recently been considerable progress in the area of using computers as a tool for theorem proving. In this paper we focus on one facet of human-computer interaction in such systems: generating natural language explanations from proofs. We first discuss the X proof system a tactic style theorem proving system for firstorder logic with a collection of inference rules corresponding to human-oriented proof techniques. In X, proofs are stored as they are discovered using a structured term representation. We describe a method for producing natural language explanations of proofs via a simple mapping algorithm from proof structures to text. Nonclassical or specialized logics are often used in specialized applications. For example, modal logics are often used to reason about time and knowledge, and inheritance theories are often developed for classification systems. The form of, and explanations for, proofs in these systems should be tailored to reflect their special features. In this paper, we focus on the extension of X to incorporate proofs in modal logic, and on the different kinds of explanations of modal proofs that can be produced to meet the needs of different users. Comments University of Pennsylvania Department of Computer and Information Science Technical Report No. MSCIS-88-18. This technical report is available at ScholarlyCommons: http://repository.upenn.edu/cis_reports/615 EXPLAINING MODAL LOGIC PROOFS Amy Felty Greg Hager MS-CIS-88-18 LINC LAB 105 Department of Computer and Information Science School of Engineering and Applied Science University of Pennsylvania Philadelphia, PA 19104