Superposition for Lambda-Free Higher-Order Logic

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 possibl...

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Bibliographic Details
Published in:	Logical methods in computer science Vol. 17, Issue 2; no. 2
Main Authors:	Bentkamp, Alexander, Blanchette, Jasmin, Cruanes, Simon, Waldmann, Uwe
Format:	Journal Article
Language:	English
Published:	Logical Methods in Computer Science Association 01.01.2021 Logical Methods in Computer Science e.V
Subjects:	Computer Science computer science - artificial intelligence computer science - logic in computer science f.4.1 i.2.3 Logic in Computer Science Boolean-free lambda-free higher-order logic refutational completeness. Extended version of Bentkamp et al "Superposition for lambda-free higher-order logic" [BBCW18] superposition calculus
ISSN:	1860-5974, 1860-5974
Online Access:	Get full text
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Summary:	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. Comment: arXiv admin note: text overlap with arXiv:2102.00453
ISSN:	1860-5974 1860-5974
DOI:	10.23638/LMCS-17(2:1)2021