Literal Trees and Resolution Technique

Abstract

The problem of mechanized deduction requires carrying out research and comparison of different methods for inference search in first-order classical logic, such as resolution-type methods, the model elimination method, the SLD-resolution, and so on. In this connection, it is desired to give a way for investigating their common and distinct features in order to use them better in theory and practice. This paper is devoted to such an investigation. Interconnection between a complete extension of the SLD-type resolution having the form of literal trees calculus and a ertain resolution technique is established. The interconnection permits to obtain some results on soundness and completeness for different resolution-type methods in the case of the weakest requirements to the factorization. In addition, when classical logic with equality is considered, it gives a possibility to make an original way for complete incorporation of the paramodulation into resolution with weak factorization as well as into the model elimination method.