Contraction-free sequent calculi for geometric theories with an application to Barr's theorem

Sequent calculus proof theory of intuitionistic apartness and order relations

Contraction-free sequent calculi for intuitionistic theories of apartness and order are given and cut-elimination for the calculi proved. Among the consequences of the result is the disjunction property for these theories. Through methods of proof analysis and permutation of rules, we establish conservativity of the theory of apartness over the theory of equality defined as the negation of apar...

Ingredients of a Deep Inference Theorem Prover

Deep inference deductive systems for classical logic provide exponentially shorter proofs than the sequent calculus systems, however with the cost of higher nondeterminism and larger search space in proof search. We report on our ongoing work on proof search with deep inference deductive systems. We present systems for classical logic where nondeterminism in proof search is reduced by constrain...

Duplication-Free Tableau Calculi Together With Cut-Free and Contraction-Free Sequent Calculi for the Interpolable . . .

Nested Sequent Calculi and Theorem Proving for Normal Conditional Logics

In this paper we focus on proof methods and theorem proving for normal conditional logics, by describing nested sequent calculi as well as a theorem prover for them. Nested sequent calculi are a useful generalization of ordinary sequent calculi, where sequents are allowed to occur within sequents. Nested sequent calculi have been profitably employed in the area of (multi)-modal logic to obtain ...

Cut elimination in the presence of axioms

Away is found to add axioms to sequent calculi that maintains the eliminability of cut, through the representation of axioms as rules of inference of a suitable form. By this method, the structural analysis of proofs is extended from pure logic to free-variable theories, covering all classical theories, and a wide class of constructive theories. All results are proved for systems in which also ...