at.logic.gapt.proofs.lkOld
An implementation of LK proof regularization. In a regular LK proof, an eigenvariable is globally unique to the proof. E.g. P(u) :- P(u) P(u) :- P(u) ----------------- fa:l ------------------- fa:l \A x:P(x) :- P(u) \A x:P(x) :- P(u) ----------------------- fa:r ------------------- fa:r \A x:P(x) :- \E x:P(x) \A x:P(x) :- \E x: P(x) --------------------------------------------------------- conj:r \A x:P(x), \A x:P(x) :- \E x:P(x) /\ \E x:P(x) --------------------------------------------------------- contr:l \A x:P(x) :- \E x:P(x) /\ \E x:P(x)
is not regular, but P(i) :- P(i) P(u) :- P(u) ----------------- fa:l ------------------- fa:l \A x:P(x) :- P(i) \A x:P(x) :- P(u) ----------------------- fa:r ------------------- fa:r \A x:P(x) :- \E x:P(x) \A x:P(x) :- \E x: P(x) --------------------------------------------------------- conj:r \A x:P(x), \A x:P(x) :- \E x:P(x) /\ \E x:P(x) --------------------------------------------------------- contr:l \A x:P(x) :- \E x:P(x) /\ \E x:P(x)
is.
Make the LK proof p regular.
An LK proof.
The regular version of proof p.
An implementation of LK proof regularization. In a regular LK proof, an eigenvariable is globally unique to the proof. E.g. P(u) :- P(u) P(u) :- P(u) ----------------- fa:l ------------------- fa:l \A x:P(x) :- P(u) \A x:P(x) :- P(u) ----------------------- fa:r ------------------- fa:r \A x:P(x) :- \E x:P(x) \A x:P(x) :- \E x: P(x) --------------------------------------------------------- conj:r \A x:P(x), \A x:P(x) :- \E x:P(x) /\ \E x:P(x) --------------------------------------------------------- contr:l \A x:P(x) :- \E x:P(x) /\ \E x:P(x)
is not regular, but P(i) :- P(i) P(u) :- P(u) ----------------- fa:l ------------------- fa:l \A x:P(x) :- P(i) \A x:P(x) :- P(u) ----------------------- fa:r ------------------- fa:r \A x:P(x) :- \E x:P(x) \A x:P(x) :- \E x: P(x) --------------------------------------------------------- conj:r \A x:P(x), \A x:P(x) :- \E x:P(x) /\ \E x:P(x) --------------------------------------------------------- contr:l \A x:P(x) :- \E x:P(x) /\ \E x:P(x)
is.