An experimental logic based on the fundamental deduction principle

Abstract

Experimental logic can be viewed as a branch of logic dealing with the actual construction of useful deductive systems and their application to various scientific disciplines. In this paper we describe an experimental deductive system called the SYMbolic EVALuator (i.e. SYMEVAL) which is based on a rather simple, yet startling principle about deduction, namely that deduction is fundamentally a process of replacing expressions by logically equivalent expressions. This principle applies both to logical and domain-dependent axioms and rules. Unlike more well-known logical inference systems which do not satisfy this principle, herein is described a system of logical axioms and rules called the SYMMETRIC LOGIC which is based on this principle. Evidence for this principle is given by proving theorems and performing deduction in the areas of set theory, logic programming, natural language analysis, program verification, automatic complexity analysis, and inductive reasoning.