arXiv subjects

Raffaele Di Donna

Publications and source records attributed to Raffaele Di Donna.

2 recordsLinked to original sources

arXiv2026

Connectivity at the crossroad of intuitionistic and classical polarizations in linear logic

We investigate a property that extends the Danos-Regnier correctness criterion for linear logic proof-structures. The property applies to the correctness graphs of a proof-structure: it states that any such graph is acyclic and the number of its connected components is exactly one more than the number of nodes bottom or weakening. This is known to be necessary but not sufficient in multiplicative exponential linear logic (MELL) to recover a sequent calculus proof from a proof-structure. We present a geometric restriction on proof-structures allowing us to turn this necessary property into a sufficient one, computationally efficient: we can thus introduce the notable fragment VMELL of MELL for which the property is indeed a correctness criterion. The fragment VMELL brings together the classical and intuitionistic polarizations. We translate the bang calculus terms into proof-nets of VMELL, factorize the usual translations in linear logic of the call-by-name and call-by-value lambda-calculi, prove that cut elimination simulates bang reduction, and provide an explicit characterization of the bang calculus terms as proof-nets.

cs.LO↗

arXiv2026

On the role of connectivity in Linear Logic proofs

We investigate a property that extends the Danos-Regnier correctness criterion for linear logic proof-structures. The property applies to the correctness graphs of a proof-structure: it states that any such graph is acyclic and the number of its connected components is exactly one more than the number of nodes bottom or weakening. This is known to be necessary but not sufficient in multiplicative exponential linear logic to recover a sequent calculus proof from a proof-structure. We present a geometric condition on untyped proof-structures allowing us to turn this necessary property into a sufficient one: we can thus isolate fragments of linear logic for which this property is indeed a correctness criterion. In a suitable fragment of multiplicative linear logic with units, the criterion yields a characterization of the equivalence induced by permutations of rules in sequent calculus. In intuitionistic linear logic, the property is equivalent to the familiar requirement of having exactly one output conclusion, and it is sufficient for sequentialization in the axiom-free setting.

cs.LO↗