Object/Class

at.logic.gapt.proofs.ceres

CERESR2LK

Related Docs: class CERESR2LK | package ceres

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object CERESR2LK extends CERESR2LK

Two implementations of first-order CERES, one (CERES) grounding the proof before the transformation, the other (CERESR2LK) performing the task inline in the Robinson2LK method.

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

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  2. final def ##(): Int

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  4. def apply(endsequent: HOLSequent, proj: Set[LKProof], rp: RobinsonResolutionProof): 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. Please note that the formulas in the different input proofs need to come from the same layer (i.e. both FOL or both HOL)

    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
    CERESR2LK
  5. 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 (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

    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
    CERESR2LK
  6. 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
    CERESR2LK
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