Proof Search Algorithm in Pure Logical Framework

Abstract

By a pure logical framework we mean a framework which does not rely on any particular formal calculus. For example, Metamath is an instance of a pure logical framework. Another example is the Russell system (https://github.com/dmitry-vlasov/russell). In this paper, we describe the proof search algorithm used in Russell. The algorithm is proved to be correct and complete, i.e. it gives only valid proofs and any valid proof can be found (up to a substitution) by the proposed algorithm.