This article introduces a logical system, called BV, which extends multiplicative linear logic
by a noncommutative self-dual logical operator. This extension is particularly challenging for …

In this thesis we see deductive systems for classical propositional and predicate logic which
use deep inference, ie inference rules apply arbitrarily deep inside formulas, and a certain …

We obtain two results about the proof complexity of deep inference:(1) Deep-inference proof
systems are as powerful as Frege ones, even when both are extended with the Tseitin …

Proof theory is the area of mathematics which studies the concepts of mathematical proof
and mathematical provability [Bus98]. It is mainly concerned with the formal syntax of logical …

We introduceatomic flows': they are graphs obtained from derivations by tracing atom
occurrences and forgetting the logical structure. We study simple manipulations of atomic …

In this paper we present a proof system that operates on graphs instead of formulas. We
begin our quest with the well-known correspondence between formulas and cographs …

In this paper I will present a deductive system for linear logic, in which all rules are local. In
particular, the contraction rule is reduced to an atomic version, and there is no global …

The calculus of structures is a new proof theoretical formalism, like natural deduction, the
sequent calculus and proof nets, for specifying logical systems syntactically. In a rule in the …

The course will give a basic introduction to deep inference, which is a design principle for
proof formalisms in which inference rules can be applied at any depth inside the proof. In …

We study a system, called NEL, which is the mixed commutative/noncommutative linear
logic BV augmented with linear logic's exponentials. Equivalently, NEL is MELL augmented …