A term calculus for the proofs in multiplicative-additive linear logic is introduced and motivated as a programming language for channel based concurrency. e term calculus is proved complete for a semantics in linearly distributive categories with additives. It is also shown that proof equivalence is decidable by showing that the cut elimination rewrites supply a conžuent rewriting system modul...

We extend the calculus of multiplicative vector fields and differential forms and their intrinsic derivatives from Lie groups to Lie groupoids; this generalization turns out to include also the classical process of complete lifting from arbitrary manifolds to tangent and cotangent bundles. Using this calculus we give a new description of the Lie bialgebroid structure associated with a Poisson g...

We consider the problem of obtaining Hennessy-Milner soundness and completeness-the coincidence of logical equivalence and bisimilarity-in the setting of transition systems with synchronous concurrent composition. Starting from a richly expressive modal logic, motivated by resource semantics and distributed systems modelling, including both additive and multiplicative propositional connectives ...

The logic of bunched implications (BI) of O’Hearn and Pym [5] is a substructural logic which freely combines additive connectives ⊃ , ∧, ∨ from propositional logic and multiplicative connectives −?, ? from linear logic. Because of its concise yet rich representation of states of resources, BI is regarded as a logic suitable for reasoning about resources. For example, by building a model for BI ...