Development of a Bidirectional Transformation Supporting Tool for Formalization with Logical Formulas and Its Application

In many applications in computer science and artificial intelligence, logical formulas are used as a formal representation to represent and/or specify various objects and relationships among them. Transforming logical formulas into informal propositional statements, e.g., declarative sentences and mathematical formulas, is important as well as transforming informal propositional statements into logical formulas. When people obtain new logical formulas as results of deduction/reasoning based on logic, investigating the obtained formulas is also not an easy task for them. Although information systems with proving, e.g., automated theorem proving systems, formal verification systems, etc., are used in various field, in the future, information systems with reasoning, e.g., automated theorem finding systems, will also be developed and used in various fields. Thus, a tool to support bidirectional transformation between informal propositional statements and logical formulas will be demanded at that time. This paper presents an implementation of a bidirectional transformation supporting tool for formalization with logical formulas. The paper also shows application of the tool in a case study of automated theorem finding with forward reasoning.