In this paper, we present a propositional sequent calculus containing disjoint copies of classical and intuitionistic logics. We prove a cut-elimination theorem and we establish a relation between this system and linear logic.

We consider a term sequent logic for the lambda-calculus. Term sequents are a judgement form similar to the logical judgement form of entailment between sentences, but denoting equality or reducibility between terms. Using term sequents, it is possible to treat lambda-terms almost like logical sentences, and to use proof-theoretic methods to establish their properties. We prove a cut-eliminatio...

We present a sequent calculus which allows the simultaneous elimination of multiple quantiiers. The approach is an improvement over the well-known skolemization in sequent calculus. It allows a lazy handling of instantiations and of the order of certain reductions. Simultaneous quantiier elimination is justiied from a semantical as well as from a proof theoretical point of view.

Providing a cut-free sequent calculus for S5 has a long history. The efforts in this direction are numerous, and each of them presents some difficulties. In this paper, we present a sequent calculus system for modal logic S5. It has in a sense subformula property. We show that the cut rule is admissible in this system.

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

In this paper we present a sequent calculus for propositional dynamic logic built using an enriched version of the tree-hypersequent method and including an infinitary rule for the iteration operator. We prove that this sequent calculus is theoremwise equivalent to the corresponding Hilbert-style system, and that it is contraction-free and cut-free. All results are proved in a purely syntactic ...