Comparing Approaches To Resolution Based Higher-Order Theorem Proving

We investigate several approaches to resolution based automated theorem proving in classical higher-order logic (based on Church’s simply typed λ-calculus) and discuss their requirements with respect to Henkin completeness and full extensionality. In particular we focus on Andrews’ higher-order resolution (Andrews 1971), Huet’s constrained resolution (Huet 1972), higher-order E-resolution, and extensional higher-order resolution (Benzmüller and Kohlhase 1997). With the help of examples we illustrate the parallels and differences of the extensionality treatment of these approaches and demonstrate that extensional higher-order resolution is the sole approach that can completely avoid additional extensionality axioms.