# Alessio Guglielmi

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 the sequent calculus, and so far, it is not achieved therein. It becomes very natural in a new formalism, called the <i>calculus of structures</i>, which is the main(More)
• ACM Trans. Comput. Log.
• 2009
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 extension rule or with the substitution rule; (2) there are analytic deep-inference proof systems that exhibit an exponential speedup over analytic Gentzen proof systems that they(More)
• CSL
• 2001
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 multiplicative linear logic, by a self-dual noncommutative operator inspired by CCS, that seems not to be expressible in the sequent calculus. Then we show that multiplicative(More)
System MV is a simple, propositional linear calculus that deals with the commutative as well as the non-commutative composition of structures. The multiplicative fragment of linear logic is a special case of MV , and the tensor rule does not suffer from unnecessary non-determinism in context partitioning as it does in the sequent calculus of linear logic.(More)
• LPAR
• 2002
We extend multiplicative exponential linear logic (MELL) by a non-commutative, self-dual logical operator. The extended system, called NEL, is defined in the formalism of the calculus of structures, which is a generalisation of the sequent calculus and provides a more refined analysis of proofs. We should then be able to extend the range of applications of(More)
• ACM Trans. Comput. Log.
• 2011
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 with the noncommutative self-dual connective seq. In this article, we show a basic compositionality property of NEL, which we call <i>decomposition</i>. This result leads to a(More)
• Mathematical Structures in Computer Science
• 2011
System NEL is the mixed commutative/non-commutative linear logic BV augmented with linear logic’s exponentials, or, equivalently, it is MELL augmented with the non-commutative self-dual connective seq. System NEL is Turingcomplete, it is able to directly express process algebra sequential composition and it faithfully models causal quantum evolution. In(More)
• Logical Methods in Computer Science
• 2008
We introduce ‘atomic flows’: they are graphs obtained from derivations by tracing atom occurrences and forgetting the logical structure. We study simple manipulations of atomic flows that correspond to complex reductions on derivations. This allows us to prove, for propositional logic, a new and very general normalisation theorem, which contains cut(More)
We study some normalisation properties of the deep-inference proof system NEL, which can be seen both as 1) an extension of multiplicative exponential linear logic (MELL) by a certain non-commutative self-dual logical operator; and 2) an extension of system BV by the exponentials of linear logic. The interest of NEL resides in: 1) its being Turing complete,(More)
Giorgio Levi has two great fortunes: he has a noble smile and he survived a heart attack. These are the important facts about his personality, and they are so evident that there is no need for this modest portrait, which does little more than stating the obvious. I should perhaps start by sketching my relation with Giorgio, so that my point of view is(More)