Alexander Bentkamp ; Jasmin Blanchette ; Simon Cruanes ; Uwe Waldmann - Superposition for Lambda-Free Higher-Order Logic

lmcs:6455 - Logical Methods in Computer Science, April 12, 2021, Volume 17, Issue 2
Superposition for Lambda-Free Higher-Order Logic

Authors: Alexander Bentkamp ; Jasmin Blanchette ; Simon Cruanes ; Uwe Waldmann

We introduce refutationally complete superposition calculi for intentional and extensional clausal $\lambda$-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 $\lambda$-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.

Volume: Volume 17, Issue 2
Published on: April 12, 2021
Submitted on: May 7, 2020
Keywords: Computer Science - Logic in Computer Science,Computer Science - Artificial Intelligence,F.4.1,I.2.3

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