Simultaneous paramodulation

Benanav, Dan

doi:10.1007/3-540-52885-7_106

Cited by 11 publications

(4 citation statements)

References 2 publications

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“…Let be the atom ordering, and assume the premises of the superposition inference are in the clause set. Instead of performing the inference, we would like to exhaustively rewrite the second premise using the first premise, to , using either demodulation or a simultaneous superposition inference [ 11 ]. Notice that the conclusion does not become redundant in this way: It is entailed by and , but is -larger than the conclusion and cannot be used.…”

Section: Preliminariesmentioning

confidence: 99%

A Comprehensive Framework for Saturation Theorem Proving

et al. 2022

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A crucial operation of saturation theorem provers is deletion of subsumed formulas. Designers of proof calculi, however, usually discuss this only informally, and the rare formal expositions tend to be clumsy. This is because the equivalence of dynamic and static refutational completeness holds only for derivations where all deleted formulas are redundant, but the standard notion of redundancy is too weak: A clause C does not make an instance $$C\sigma $$ C σ redundant. We present a framework for formal refutational completeness proofs of abstract provers that implement saturation calculi, such as ordered resolution and superposition. The framework modularly extends redundancy criteria derived via a familiar ground-to-nonground lifting. It allows us to extend redundancy criteria so that they cover subsumption, and also to model entire prover architectures so that the static refutational completeness of a calculus immediately implies the dynamic refutational completeness of a prover implementing the calculus within, for instance, an Otter or DISCOUNT loop. Our framework is mechanized in Isabelle/HOL.

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Section: Preliminariesmentioning

confidence: 99%

A Comprehensive Framework for Saturation Theorem Proving

et al. 2022

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“…Nonetheless, the redundant inferences below are a strict subset of the redundant inferences of our report and thus completeness also holds using the notion below. For the few prover optimizations based on inference redundancy that we know about (e.g., simultaneous superposition [4]), the following criterion suffices.…”

Section: Finally Applying Eres Twice and Falseelim Once Yields The Empty Clausementioning

confidence: 99%

Superposition for Full Higher-order Logic

Bentkamp

Blanchette

Tourret

et al. 2021

Automated Deduction – CADE 28

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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 from the interplay between $$\lambda $$ λ -terms and Booleans. Our implementation in Zipperposition outperforms all other higher-order theorem provers and is on a par with an earlier, pragmatic prototype of Booleans in Zipperposition.

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“…We keep this definition as well, but we use a nonstandard notion of ground instances for some of the Boolean rules. In our report, we define a slightly stronger variant of inference redundancy via an explicit ground calculus, but the following notion is also strong enough to justify the few prover optimizations based on inference redundancy we know from the literature (e.g., simultaneous superposition [7]).…”

Section: Definition 1 (Selection Functions)mentioning

confidence: 99%

Superposition with First-class Booleans and Inprocessing Clausification

Nummelin

Bentkamp

Tourret

et al. 2021

Automated Deduction – CADE 28

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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.

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Simultaneous paramodulation

Cited by 11 publications

References 2 publications

A Comprehensive Framework for Saturation Theorem Proving

A Comprehensive Framework for Saturation Theorem Proving

Superposition for Full Higher-order Logic

Superposition with First-class Booleans and Inprocessing Clausification

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