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This paper introduces Formath (Formalising Mathematics), a new formalization of higher-order logic which aims to be more attractive to mathematicians. The paper concentrates on the syntax, semantics, deduction rules, axioms, and the proofs of soundness and consistency. Comparisons are also given with other systems for higher-order logic, and this is supported by examples. First, the author introduces the universe U, giving the basic and standard universes, and states that U can be formalized in ZFC. Thereafter, the syntax of types is introduced using type-structures where compound types contain both the atomic and the function types. The semantics of the types is then given and this is followed by the syntax and semantics of terms. Then, basic and standard type and term structures and models are introduced. This is followed by the basic and standard axioms and theories and their extensions. Throughout, one sees that symmetry is paramount. The deduction rules as well as the basic and standard axioms and the type and term extensions are shown to be sound. Comparisons with other HOL systems are given and this is followed by some example derivations in Formath. Formath indeed seems to be an attractive formalization which enjoys a number of advantages which are discussed well in the paper

Year: 2013

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