Superposition for Lambda-Free Higher-Order Logic
This work addresses the challenge of automated reasoning in higher-order logic for theorem proving communities, representing an incremental advancement toward broader applications.
The authors tackled the problem of automated theorem proving for λ-free higher-order logic by introducing refutationally complete superposition calculi, which were implemented in the Zipperposition prover and evaluated on benchmarks, showing promising results as a step toward efficient provers for full higher-order logic.
We introduce refutationally complete superposition calculi for intentional and extensional clausal $λ$-free higher-order logic, two formalisms that allow partial application and applied variables. The calculi are parameterized by a term order that need not be fully monotonic, making it possible to employ the $λ$-free higher-order lexicographic path and Knuth-Bendix orders. We implemented the calculi in the Zipperposition prover and evaluated them on Isabelle/HOL and TPTP benchmarks. They appear promising as a stepping stone towards complete, highly efficient automatic theorem provers for full higher-order logic.