System for Automated Deduction (SAD): Linguistic and Deductive Peculiarities

In this paper a state-of-the-art of a system for automated deduction called SAD is described *. An architecture of SAD corresponds well to a modern vision of the Evidence Algorithm programme advanced by Academician V.Glushkov. The system is intended for accumulating mathematical knowledge and using it in a regular and efficient manner for processing a self-contained mathematical text in order to prove a given statement that always is considered as a part of the text. Two peculiarities are inherent in SAD: (a) mathematical texts under consideration are formalized using a specific formal language, which is close to natural languages from usual mathematical publications; (b) proof search is based on a specific sequenttype calculus, which gives a possibility to formalize “natural reasoning style”. The language may be used as a tool to write and to verify mathematical papers, theorems, and formal specifications, to perform model checking, and so on. The calculus is oriented to constructing some natural proof search methods such as definition and auxiliary proposition applications.