2022/07/12 by Steven Obua, Obua, Steven
Computer Science · #Computability, Logic, AI Algorithms #FOS: Computer and information sciences #Logic in Computer Science (cs.LO) #Logic, Reasoning, and Knowledge #Logic, programming, and type systems
paper · pdf · doi:10.48550/arxiv.2207.05610
openalex publication_date 2022/07/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Abstraction logic is a new logic, serving as a foundation of mathematics. It combines features of both predicate logic and higher-order logic: abstraction logic can be viewed both as higher-order logic minus static types as well as predicate logic plus operators and variable binding. We argue that abstraction logic is the best foundational logic possible because it maximises both simplicity and practical expressivity. This argument is supported by the observation that abstraction logic has simpler terms and a simpler notion of proof than all other general logics. At the same time, abstraction logic can formalise both intuitionistic and classical abstraction logic, and is sound and complete for these logics and all other logics extending deduction logic with equality.