Superposition for Full Higher-order Logic

@inproceedings{Bentkamp2021SuperpositionFF,
  title={Superposition for Full Higher-order Logic},
  author={Alexander Bentkamp and Jasmin Christian Blanchette and Sophie Tourret and Petar Vukmirovi{\'c}},
  booktitle={CADE},
  year={2021}
}
We recently designed two calculi as stepping stones towards superposition for full higher-order logic: Boolean-free $$\lambda $$ λ -superposition and superposition for first-order logic with interpreted Booleans. Stepping on these stones, we finally reach a sound and refutationally complete calculus for higher-order logic with polymorphism, extensionality, Hilbert choice, and Henkin semantics. In addition to the complexity of combining the calculus’s two predecessors, new challenges arise… 

Superposition for Higher-Order Logic

We recently designed two calculi as stepping stones towards superposition for full higher-order logic: Boolean-free λ-superposition and superposition for first-order logic with interpreted Booleans.

Superposition with First-class Booleans and Inprocessing Clausification

A complete superposition calculus for first-order logic with an interpreted Boolean type to lay the foundation for refutationally complete calculi in more expressive logics with Booleans, and to make superposition work efficiently on problems that would be obfuscated when using clausification as preprocessing.

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This work designs a sound and refutationally complete calculus for higher-order logic with polymorphism, extensionality, Hilbert choice, and Henkin semantics, and implements its implementation in Zipperposition on a par with an earlier, pragmatic prototype of Booleans.

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Techniques that address issues such as infinitely branching inference rules, new possibilities such as reasoning about Booleans, and the need to curb the explosion of specific higher-order rules are described and evaluated in the Zipperposition theorem prover.

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