Object/Class

at.logic.gapt.proofs.ceres

CERES

Related Docs: class CERES | package ceres

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object CERES extends CERES

This implementation of the CERES method does the proof reconstruction via Robinson2LK.

Source
CERES.scala
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  1. final def !=(arg0: Any): Boolean

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  2. final def ##(): Int

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  3. final def ==(arg0: Any): Boolean

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  4. def apply(endsequent: HOLSequent, proj: Set[LKProof], rp: ResolutionProof): LKProof

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    Applies the CERES method to a first order proof with equality.

    Applies the CERES method to a first order proof with equality. Internally this is handled by the RobinsoToLK method.

    endsequent

    The end-sequent of the original proof

    proj

    The projections of the original proof

    rp

    A resolution refutation

    returns

    an LK Proof in Atomic Cut Normal Form (ACNF) i.e. without quantified cuts

    Definition Classes
    CERES
  5. def apply(p: LKProof, pred: (HOLFormula) ⇒ Boolean, prover: ResolutionProver): LKProof

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    CERES
  6. def apply(p: LKProof, pred: (HOLFormula) ⇒ Boolean): LKProof

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    Applies the CERES method to a first order proof with equality.

    Applies the CERES method to a first order proof with equality. Internally this is handled by the RobinsoToLK method.

    p

    a first-order LKProof without strong quantifiers in the end-sequent (i.e. structural rules, cut, logical rules, equational rules but no definitions, schema,higher order)

    pred

    a predicate to specify which cut formulas to eliminate (e.g. x => containsQuantifiers(x) to keep propositional cuts intact)

    returns

    an LK Proof in Atomic Cut Normal Form (ACNF) i.e. without quantified cuts

    Definition Classes
    CERES
  7. def apply(p: LKProof, prover: ResolutionProver): LKProof

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    Definition Classes
    CERES
  8. def apply(p: LKProof): LKProof

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    Applies the CERES method to a first order proof with equality.

    Applies the CERES method to a first order proof with equality. Internally this is handled by the RobinsoToLK method.

    p

    a first-order LKProof (structural rules, cut, logical rules, equational rules but no definitions, schema,higher order) also each formula must be a FOLFormula, since the prover9 interface returns proofs from the FOL layer

    returns

    an LK Proof in Atomic Cut Normal Form (ACNF) i.e. without quantified cuts

    Definition Classes
    CERES
  9. final def asInstanceOf[T0]: T0

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  10. def clone(): AnyRef

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  11. final def eq(arg0: AnyRef): Boolean

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  12. def equals(arg0: Any): Boolean

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  13. def finalize(): Unit

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  14. def findMatchingProjection(endsequent: HOLSequent, projections: Set[LKProof])(axfs: HOLSequent): LKProof

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  15. final def getClass(): Class[_]

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  16. def hashCode(): Int

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  17. final def isInstanceOf[T0]: Boolean

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  18. final def ne(arg0: AnyRef): Boolean

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  19. final def notify(): Unit

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  20. final def notifyAll(): Unit

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  21. def refProjection(es: HOLSequent): LKProof

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    CERES
  22. def skipEquations: (HOLFormula) ⇒ Boolean

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    True if the formula is not an equation.

    True if the formula is not an equation. Intended use: predicate argument of CERES. In case the only cuts on equations come from a translation of binary equation rules to unary ones, this should provide the same clause sets and projections as the binary rules.

  23. def skipNothing: (HOLFormula) ⇒ Boolean

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  24. def skipPropositional: (HOLFormula) ⇒ Boolean

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    True if the formula is propositional and does not contain free variables other than type i.

    True if the formula is propositional and does not contain free variables other than type i. Intended use: predicate argument of CERES. In case the only cuts on equations come from a translation of binary equation rules to unary ones, this should provide the same clause sets and projections as the binary rules.

  25. final def synchronized[T0](arg0: ⇒ T0): T0

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  26. def toString(): String

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  27. final def wait(): Unit

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  28. final def wait(arg0: Long, arg1: Int): Unit

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  29. final def wait(arg0: Long): Unit

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Inherited from CERES

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