INTRODUCING TYPES INTO ELEMENTARY FORMAL SYSTEMS

The elementary formal systems (EFS's for short) work as a theoretical basis in the various fields of computer science such as formal language theory, programming semantics, machine learning and so on. In this paper, we first define proof figures which illustrate proofs of EFS and show standard proof figures for ground atoms which are distinctive in the usage of inference rules. Then we formalize typed EFS, which is a natural extension of EFS obtained by replacing variables by typed variables and show some basic properties as a logic programming language. Finally, we illustrate the first order logic in term of our typed EFS's.