A Parigot-style linear -calculus for full intuitionistic linear logic.
Coherence of Proof-net Categories
Coherence of the double involution on -autonomous categories.
Entropic Hopf algebras and models of non-commutative logic.
Exploring the gap between linear and classical logic.
Karp-Miller trees for a branching extension of VASS.
Models of linear logic
Morphisms and modules for poly-bicategories.
Natural deduction and coherence for non-symmetric linearly distributive categories.
Polarized category theory, modules, and game semantics.
Preface to the special volume: “Chu spaces: theory and applications".
Quantum B-algebras
The concept of quantale was created in 1984 to develop a framework for non-commutative spaces and quantum mechanics with a view toward non-commutative logic. The logic of quantales and its algebraic semantics manifests itself in a class of partially ordered algebras with a pair of implicational operations recently introduced as quantum B-algebras. Implicational algebras like pseudo-effect algebras, generalized BL- or MV-algebras, partially ordered groups, pseudo-BCK algebras, residuated posets,...
Quantum coherent spaces and linear logic
Quantum Coherent Spaces were introduced by Girard as a quantum framework where to interpret the exponential-free fragment of Linear Logic. Aim of this paper is to extend Girard's interpretation to a subsystem of linear logic with bounded exponentials. We provide deduction rules for the bounded exponentials and, correspondingly, we introduce the novel notion of bounded exponentials of Quantum Coherent Spaces. We show that the latter provide a categorical model of our system. In order to do that,...
Quantum coherent spaces and linear logic
Quantum Coherent Spaces were introduced by Girard as a quantum framework where to interpret the exponential-free fragment of Linear Logic. Aim of this paper is to extend Girard's interpretation to a subsystem of linear logic with bounded exponentials. We provide deduction rules for the bounded exponentials and, correspondingly, we introduce the novel notion of bounded exponentials of Quantum Coherent Spaces. We show that the latter provide a categorical model of our system. In order to do that,...
The Dialectica interpretation of first-order classical affine logic.
The Frobenius relations meet linear distributivity.