kolmogorov

gapt.proofs.nd.kolmogorov
object kolmogorov

Attributes

Source
transformation.scala
Graph
Supertypes
class Object
trait Matchable
class Any
Self type
kolmogorov.type

Members list

Value members

Concrete methods

def apply(proof: NDProof): NDProof

Applies the Kolmogorov proof transformation to a given natural deduction proof. The transformation removes all occurences of the excluded middle rule and the botttom elimination rule, and thus the resulting proof is a proof in intuitionistic, minimal logic. The conclusion of the resulting proof is the Kolmogorov trnaslation k applied to the original conclusion.

Applies the Kolmogorov proof transformation to a given natural deduction proof. The transformation removes all occurences of the excluded middle rule and the botttom elimination rule, and thus the resulting proof is a proof in intuitionistic, minimal logic. The conclusion of the resulting proof is the Kolmogorov trnaslation k applied to the original conclusion.

Value parameters

proof

A proof in ND for a sequent Γ :- A

Attributes

Returns

A proof in intuitionistic, minimal ND for the sequent k(Γ) :- k(A)

Source
transformation.scala
def k(formula: Expr): Formula

Applies the Kolmogorov translation k to a formula. This function puts a double negation in front of every subformula, in case this subformula is not negated already.

Applies the Kolmogorov translation k to a formula. This function puts a double negation in front of every subformula, in case this subformula is not negated already.

Value parameters

formula

input formula for the function k

Attributes

Returns

result of applying k to the input formula

Source
transformation.scala