According to the classical consistency presupposition, contradictions have an explosive
character: Whenever they are present in a theory, anything goes, and no sensible reasoning …

In this paper we introduce a new natural deduction system for the logic of lattices, and a
number of extensions of lattice logic with different negation connectives. We provide the …

It is well-known that the size of propositional classical proofs can be huge. Proof theoretical
studies discovered exponential gaps between normal or cut free proofs and their respective …

The geometric system of deduction called N-Graphs was introduced by de Oliveira in 2001.
The proofs in this system are represented by means of digraphs and, while its derivations …

This paper presents a linear time algorithm for proof verification on N-Graphs. This system,
introduced by de Oliveira, incorporates the geometrical techniques from the theory of proof …

Kneale observed that Gentzen's calculus of natural deductions NK for classical logic is not
symmetric and has unnecessarily complicated hypothetical inference rules. Kneale …

Since proof-nets for MLL− were introduced by Girard (1987), several studies have been
made on its soundness proof. Bellin & Van de Wiele (1995) produced an elegant proof …

Alves presented in his PhD thesis a normalization procedure for N-Graphs, a multiple
conclusion natural deduction for propositional classical logic proposed by de Oliveira in …

Traditional proof theory of Propositional Logic deals with proofs whose size can be huge.
Proof theoretical studies discovered exponential gaps between normal or cut free proofs and …

N-Graphs is a multiple conclusion natural deduction with proofs as directed graphs,
motivated by the idea of proofs as geometric objects and aimed towards the study of the …