Every language recognized by the Lambek calculus with brackets is context-free. This is shown by combining an observation by Jäger with an entirely straightforward adaptation of the method Pentus used for the original Lambek calculus. The case of the variant of the calculus allowing sequents with empty antecedents is slightly more complicated, requiring a restricted use of the multiplicative unit.

This paper is included in a series aiming to contribute to the algebraic theory of distributed computation. The key problem in understanding Multi-Agent Systems is to find a theory which integrates the reactive part and the control part of such systems. To this end we use the calculus of flownomials. It is a polynomial-like calculus for representing flowgraphs and their behaviours. An ‘additive...

We study the discrete logarithm problem for the multiplicative group and for elliptic curves over a finite field by using a lifting of the corresponding object to an algebraic number field and global duality. We introduce the signature of a Dirichlet character (in the multiplicative group case) or principal homogeneous space (in the elliptic curve case), which is a measure of the ramification a...

We give a simple term calculus for the multiplicative exponential fragment of Classical Linear Logic, by extending Barber and Plotkin’s system for the intuitionistic case. The calculus has the nonlinear and linear implications as the basic constructs, and this design choice allows a technically managable axiomatization without commuting conversions. Despite this simplicity, the calculus is show...

We provide an alternative proof of the sequentialisation theorem for proof nets of multiplicative linear logic. Namely, we show how a proof net can be transformed into a sequent calculus proof simply by properly adding to it some special edges, called sequential edges, which express the sequentiality constraints given by sequent calculus. © 2008 Elsevier B.V. All rights reserved.

We prove that for both the Lambek calculus L and the Lambek calculus allowing empty premises L∗ the derivability problem is NP-complete. It follows that also for the multiplicative fragments of cyclic linear logic and noncommutative linear logic the derivability problem is NP-complete.

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...