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 …

We see a systematic set of cut-free axiomatisations for all the basic normal modal logics
formed by some combination the axioms d, t, b, 4, 5. They employ a form of deep inference …

Many modern applications of description logics (DLs) require answering queries over large
data quantities, structured according to relatively simple ontologies. For such applications …

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 introduce the calculus of structures: it is more general than the sequent calculus and it
allows for cut elimination and the subformula property. We show a simple extension of …

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 usual proof systems, like the sequent calculus, only a very limited way of combining proofs
is available through the tree structure. We present in this paper a logic-independent proof …

This is a book in categorial (or categorical) proof theory, a field of general proof theory at the
border between logic and category theory. In this field the language, more than the methods …