We present new variants of known proofs of cut elimination for intui-tionistic and classical sequent calculi. In both cases the proofs proceed by three nested structural inductions, avoiding the explicit use of multi-sets and termination measures on sequent derivations. This makes them amenable to elegant and concise representations in LF, which are given in full detail.

Basic proof search tactics in logic and type theory can be seen as the rootrst applications of rules in an appropriate sequent calculus, preferably without the redundancies generated by permutation of rules. This paper addresses the issues of de ning such sequent calculi for Pure Type Systems (PTS, which are based on natural deduction) and then organizing their rules for effective proof search....

Unfortunately first-order logic has certain limitations which are felt in many applications such as in hardware verification. The use of proof assistants like the HOL sys tem ([Gord88]) is therefore resorted to. However many theorems of higher order logic can also be proven by methods of first order logic as well. Being aware of this situation, we have implemented a prover based on Sequent Calc...

This paper tries to remove what seems to be the remaining stumbling blocks in the way to a full understanding of the Curry-Howard isomorphism for sequent calculus, namely the questions: What do variables in proof terms stand for? What is co-control and a co-continuation? How to define the dual of Parigot’s mu-operator so that it is a co-control operator? Answering these questions leads to the i...

The count invariance of van Benthem (1991[16]) is that for a sequent to be a theorem of the Lambek calculus, for each atom, the number of positive occurrences equals the number of negative occurrences. (The same is true for multiplicative linear logic.) The count invariance provides for extensive pruning of the sequent proof search space. In this paper we generalize count invariance to categori...

BACKGROUND Many all-inside suture-based devices are currently available, including the Meniscal Cinch, FasT-Fix, Ultra FasT-Fix, RapidLoc, MaxFire, and CrossFix System. These different devices have been compared in various configurations, but to our knowledge, the Sequent meniscal repair device, which applies running sutures, has not been compared with the Ultra FasT-Fix, nor has it been compar...

On one hand, traditional tableau systems for temporal logic (TL) generate an auxiliary graph that must be checked and (possibly) pruned in a second phase of the refutation procedure. On the other hand, traditional sequent calculi for TL make use of a kind of inference rules (mainly, invariant-based rules or infinitary rules) that complicates their automatization. A remarkable consequence of usi...

A construction principle for natural deduction systems for arbitrary finitely-many-valued first order logics is exhibited. These systems are systematically obtained from sequent calculi, which in turn can be automatically extracted from the truth tables of the logics under consideration. Soundness and cut-free completeness of these sequent calculi translate into soundness, completeness and norm...

We provide an alternative proof of the sequentialisation theorem for proof nets of multiplicative linear logic. Namely, we show how a proof net can be transformed into a sequent calculus proof simply by properly adding to it some special edges, called sequential edges, which express the sequentiality constraints given by sequent calculus. © 2008 Elsevier B.V. All rights reserved.

Development of a contraction-free BI sequent calculus, be it in the sense of G3i or G4i, has not been successful in literature. We address the open problem by presenting such a sequent system. In fact our calculus involves no structural rules.