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Conference Papers Year : 2021

Superposition with First-class Booleans and Inprocessing Clausification

Abstract

We present a complete superposition calculus for first-order logic with an interpreted Boolean type. Our motivation is to lay the foundation for refutationally complete calculi in more expressive logics with Booleans, such as higher-order logic, and to make superposition work efficiently on problems that would be obfuscated when using clausification as preprocessing. Working directly on formulas, our calculus avoids the costly axiomatic encoding of the theory of Booleans into first-order logic and offers various ways to interleave clausification with other derivation steps. We evaluate our calculus using the Zipperposition theorem prover, and observe that, with no tuning of parameters, our approach is on a par with the state-of-the-art approach.

Dates and versions

hal-03552065 , version 1 (02-02-2022)

Identifiers

Cite

Visa Nummelin, Alexander Bentkamp, Sophie Tourret, Petar Vukmirović. Superposition with First-class Booleans and Inprocessing Clausification. CADE 2021 - 28th International Conference on Automated Deduction, Jul 2021, Pittsburgh, PA / online, United States. pp.378-395, ⟨10.1007/978-3-030-79876-5_22⟩. ⟨hal-03552065⟩
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