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Linear Logic 4] has raised a lot of interest in computer research, especially because of its resource sensitive nature. One line of research studies proof construction procedures and their interpretation as computational models, in the \Logic Programming" tradition. An eecient proof search procedure, based on a proof normaliza-tion result called \Focusing",… (More)

- Roberto Maieli, Quintijn Puite
- Arch. Math. Log.
- 2005

- Roberto Maieli
- Arch. Math. Log.
- 2003

We introduce a new correctness criterion for multiplicative non commutative proof nets which can be considered as the non-commutative counterpart to the Danos-Regnier criterion for proof nets of linear logic. The main intuition relies on the fact that any switching for a proof net (obtained by mutilating one premise of each disjunction link) can be… (More)

- Olivier Laurent, Roberto Maieli
- 2008 23rd Annual IEEE Symposium on Logic in…
- 2008

We present a syntax for MALL (multiplicative additive linear logic without units) proof nets which refines Girard's one. It is also based on the use of monomial weights for identifying additive components (slices). Our generalization gives the possibility of representing a kind of sharing of nodes which does not exist in Girard's nets. This sharing leads to… (More)

- Roberto Maieli
- LPAR
- 2007

Proof nets are a parallel syntax for sequential proofs of linear logic, firstly introduced by Girard in 1987. Here we present and intrinsic (geometrical) characterization of proof nets, that is a correctness criterion (an algorithm) for checking those proof structures which correspond to proofs of the purely multiplicative and additive fragment of linear… (More)

- Roberto Maieli, Paul Ruet
- Inf. Comput.
- 2003

It is now well-established that the so-called focalization property plays a central role in the design of programming languages based on proof search, and more generally in the proof theory of linear logic. We present here a sequent calculus for non-commutative logic (NL) which enjoys the focalization property. In the multiplicative case, we give a… (More)

- Jean-Marc Andreoli, Roberto Maieli, Paul Ruet
- Ann. Pure Appl. Logic
- 2006

This work presents a computational interpretation of the construction process for cyclic (CyLL) and non-commutative (NL) sequential proofs. We assume a proof construction paradigm, based on a normalisation procedure, known as focussing which manages efficiently the non-determinism of the construction. Similarly to the commutative case, a new formulation of… (More)

- V. Michele Abrusci, Roberto Maieli
- WoLLIC
- 2015

- Roberto Maieli
- RTA-TLCA
- 2014

In this work we present a paradigm of focusing proof search based on an incremental construction of retractile (i.e, correct or sequentializable) proof structures of the pure (units free) multiplicative and additive fragment of linear logic. The correctness of proof construction steps (or expansion steps) is ensured by means of a system of graph retraction… (More)

- V. Michele Abrusci, Roberto Maieli
- FG
- 2015

This paper concerns a logical approach to natural language parsing based on proof nets (PNs), i.e. de-sequentialized proofs, of linear logic (LL). It first provides a syntax for proof structures (PSs) of the cyclic multiplicative and additive fragment of linear logic (CyMALL). A PS is an oriented graph, weighted by boolean monomial weights, whose… (More)