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 - https://doi.org/10.23638/LMCS-17(2:1)2021
Superposition for Lambda-Free Higher-Order LogicArticle

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
    Accepted on: February 11, 2021
    Submitted on: May 7, 2020
    Keywords: Computer Science - Logic in Computer Science,Computer Science - Artificial Intelligence,F.4.1,I.2.3
    Funding:
      Source : OpenAIRE Graph
    • Fast Interactive Verification through Strong Higher-Order Automation; Funder: European Commission; Code: 713999

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