The paper presents a way to transform pregroup grammars into contextfree grammars using functional composition. The same technique can also be used for the proof-nets of multiplicative cyclic linear logic and for Lambek calculus allowing empty premises.

In this paper, a novel variational model with strict convexity for removing multiplicative noise from images is proposed and studied. Firstly, by applying maximum likelihood estimation method and the Bayesian formulation, the variational model is derived. Then, we use an alternating minimization algorithm to find out the minimizer of the objective function, and prove the existence of the minimi...

The aim of this paper is to show that under some mild conditions a functional equation of multiplicative $(alpha,beta)$-derivation is superstable on standard operator algebras. Furthermore, we prove that this generalized derivation can be a continuous and an inner $(alpha,beta)$-derivation.

We examine ‘weak-distributivity’ as a rewriting rule ; WD defined on multiplicative proof-structures (so, in particular, on multiplicative proof-nets: MLL). This rewriting does not preserve the type of proofsnets, but does nevertheless preserve their correctness. The specific contribution of this paper, is to give a direct proof of completeness for ; WD : starting from a set of simple generator...

We consider a classical (propositional) version, CBI, of O’Hearn and Pym’s logic of bunched implications (BI) from a modeland prooftheoretic perspective. We present a class of classical models of BI which extend the usual BI-models, based on partial commutative monoids, with an algebraic notion of “resource negation”. This class of models gives rise to natural definitions of multiplicative fals...

The calculus of structures is a proof theoretical formalism which generalizes the sequent calculus with the feature of deep inference: In contrast to the sequent calculus, inference rules can be applied at any depth inside a formula, bringing shorter proofs than any other formalisms supporting analytical proofs. However, deep applicability of the inference rules causes greater nondeterminism th...

We present two rewriting systems that define labelled explicit substitution λ -calculi. Our work is motivated by the close correspondence between Lévy’s labelled λ -calculus and paths in proof-nets, which played an important role in the understanding of the Geometry of Interaction. The structure of the labels in Lévy’s labelled λ -calculus relates to the multiplicative information of paths; the...

We present Classical BI (CBI), a new addition to the family of bunched logics which originates in O’Hearn and Pym’s logic of bunched implications BI. CBI differs from existing bunched logics in that its multiplicative connectives behave classically rather than intuitionistically (including in particular a multiplicative version of classical negation). At the semantic level, CBI-formulas have th...

The connection between stochastic differential equations and associated Fokker-Planck equations is elucidated by the full functional calculus. One-variable equations with either additive or multiplicative noise are considered. The central focus is on approximate Fokker-Planck equations which describe the consequences of using "colored" noise, which has an exponential correlation function and a ...