Terms for Natural Deduction, Sequent Calculus and Cut Elimination in Classical Logic
نویسندگان
چکیده
This paper revisits the results of Barendregt and Ghilezan [3] and generalizes them for classical logic. Instead of λ-calculus, we use here λμ-calculus as the basic term calculus. We consider two extensionally equivalent type assignment systems for λμ-calculus, one corresponding to classical natural deduction, and the other to classical sequent calculus. Their relations and normalisation properties are investigated. As a consequence a short proof of Cut elimination theorem is obtained.
منابع مشابه
Complexity Analysis of Cut Elimination in First Order Based Logics
The worst-case complexity of cut elimination in sequent calculi for first order based logics is investigated in terms of the increase in logical depth of the deduction. It is shown that given a calculus satisfying a general collection of sufficient conditions for cut elimination and given a deduction with cuts, there exists a cut free deduction with a logical depth, in the worst case, hyper-exp...
متن کاملAtomic Cut Elimination for classical Logic
System SKS is a set of rules for classical propositional logic presented in the calculus of structures. Like sequent systems and unlike natural deduction systems, it has an explicit cut rule, which is admissible. In contrast to sequent systems, the cut rule can easily be restricted to atoms. This allows for a very simple cut elimination procedure based on plugging in parts of a proof, like norm...
متن کاملPropositional Calculus in Coq
I formalize important theorems about classical propositional logic in the proof assistant Coq. The main theorems I prove are (1) the soundness and completeness of natural deduction calculus, (2) the equivalence between natural deduction calculus, Hilbert systems and sequent calculus and (3) cut elimination for sequent calculus.
متن کاملRevisiting the Correspondence between Cut Elimination and Normalisation
Cut-free proofs in Herbelin’s sequent calculus are in 1-1 correspondence with normal natural deduction proofs. For this reason Herbelin’s sequent calculus has been considered a privileged middle-point between L-systems and natural deduction. However, this bijection does not extend to proofs containing cuts and Herbelin observed that his cutelimination procedure is not isomorphic to β-reduction....
متن کاملOn a Local-Step Cut-Elimination Procedure for the Intuitionistic Sequent Calculus
In this paper we investigate, for intuitionistic implicational logic, the relationship between normalization in natural deduction and cut-elimination in a standard sequent calculus. First we identify a subset of proofs in the sequent calculus that correspond to proofs in natural deduction. Then we define a reduction relation on those proofs that exactly corresponds to normalization in natural d...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1992