On the calculus of positively constructed formulas for automated theorem proving

Abstract

The paper deals with an expressive logic language LF and its calculus. Formulas of this language consist of some large-scale structural elements, such as type quantifiers. The language LF contains only two logic symbols—∀ and ∃, which form the set of logic connectives of the language. The logic calculus JF and complete strategy for automated proof search based on a single unary rule of inference are considered. This calculus has a number of other features which lead to the reduction of the combinatorial complexity of finding the deductions in comparison to the known systems for automated theorem proving as the Resolution method and Genzen calculus. Problems of effective implementation of JF as a program system for automated theorem proving are considered.