The Higher-Order-Logic Formath

Abstract

We introduce a new formalization of Higher-Order-Logic (abbreviated Hol), which we baptized Formath, an acronym for FORMAl MATHematics. We discuss the syntax, semantics, deduction-rules, axioms and principles of extension, after which we prove soundness and consistency. The semantics are comparable to other systems for Hol, such as Hol-4 and Hol-Light, but other parts differ from the traditional way of working, for example the deduction-rules and axioms. We discuss these differences in large extent. We also talk about porting theorems to the Formath library, provide examples and discuss the applications.