Structural proof theory is a branch of logic that studies the general structure and properties of
logical and mathematical proofs. This book is both a concise introduction to the central …

A general method for generating contraction-and cut-free sequent calculi for a large family of
normal modal logics is presented. The method covers all modal logics characterized by …

The axiomatic presentation of modal systems and the standard formulations of natural
deduction and sequent calculus for modal logic are reviewed, together with the difficulties …

A FORMAL SYSTEM FOR EUCLID’S ELEMENTS Page 1 THE REVIEW OF SYMBOLIC LOGIC
Volume 2, Number 4, December 2009 A FORMAL SYSTEM FOR EUCLID’S ELEMENTS …

Using labelled formulae, a cut-free sequent calculus for intuitionistic propositional logic is
presented, together with an easy cut-admissibility proof; both extend to cover, in a uniform …

Geometric theories are presented as contraction-and cut-free systems of sequent calculi with
mathematical rules following a prescribed rule-scheme that extends the scheme given in …

In this survey paper, we present several results linking quantifier-free axiomatizations of
various Euclidean and hyperbolic geometries in languages without relation symbols to …

Although sequent calculi constitute an important category of proof systems, they are not as
well known as axiomatic and natural deduction systems. Addressing this deficiency, this …

An important application of focused variants of Gentzen's sequent calculus proof rules is the
construction of (possibly) large synthetic inference rules. This paper examines the synthetic …

Proofs and countermodels are the two sides of completeness proofs, but, in general, failure
to find one does not automatically give the other. The limitation is encountered also for …