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at.logic.gapt.proofs.lk

Interpolate

object Interpolate

Source
applyInterpolation.scala
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  4. def apply(p: LKProof, color: Sequent[Boolean]): (LKProof, LKProof, Formula)

    This method computes interpolating proofs from propositional LK-proof containing at most atomic cuts.

    This method computes interpolating proofs from propositional LK-proof containing at most atomic cuts. As arguments it expects a proof p and a partition of its end-sequent into two parts: a "negative" part and a "positive" part. For \Gamma |- \Delta being the negative and \Pi |- \Lambda being the positive part, it will compute an interpolant I and proofs of \Gamma |- \Delta, I and I, \Pi |- \Lambda

    p

    the LK proof from which the interpolant is to be extracted

    color

    indicates which formulas are in the positive part

    returns

    a triple consisting of ( a proof of \Gamma |- \Delta, I, a proof of I, \Pi |- \Lambda, the FOLFormula I )

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