This paper shows how derivations in (a variation of) SKS can be translated into proof nets. Since an SKS derivation contains more information about a proof than the corresponding proof net, we observe a loss of information which can be understood as “eliminating bureaucracy”. Technically this is achieved by cut reduction on proof nets. As an intermediate step between the two extremes, SKS deriv...

This paper introduces deriuation table.s that represent a complete grammatical derivations as whole in a vertical way. These tables are obtained by writing the consecutive sentential forms of grammatical derivations vertically one by one. The present paper places and discusses some restrictions on the columns of these tables. IVIore specifically, these restrictions constrain the order of contex...

We survey some old and new results in the theory of derivations on Banach algebras. Although our overview is broad ranging, our principal interest is in recent results concerning conditions on a derivation implying that its range is contained in the radical of the algebra. In this paper we present a survey of some aspects of the theory of derivations on Banach algebras. No attempt is made at co...

We propose a study of the modes of derivation of higher-order recursion schemes, proving that value trees obtained from schemes using innermost-outermost derivations (IO) are the same as those obtained using unrestricted derivations. Given that higher-order recursion schemes can be used as a model of functional programs, innermost-outermost derivations policy represents a theoretical view point...

This paper shows how derivations in (a variation of) SKS can be translated into proof nets. Since an SKS derivation contains more information about a proof than the corresponding proof net, we observe a loss of information which can be understood as “eliminating bureaucracy”. Technically this is achieved by cut reduction on proof nets. As an intermediate step between the two extremes, SKS deriv...

Given a categorical crossed module H→ G, where G is a group, we show that the category of derivations, Der(G,H), from G into H has a natural monoidal structure. We introduce the Whitehead categorical group of derivations as the Picard category of Der(G,H) and then we characterize the invertible derivations, with respect to the tensor product, in this monoidal category. 2000 Mathematics Subject ...

Let $mathfrak{A}$ be a Banach algebra. We say that a sequence ${D_n}_{n=0}^infty$ of continuous operators form $mathfrak{A}$ into $mathfrak{A}$ is a textit{local higher derivation} if to each $ainmathfrak{A}$ there corresponds a continuous higher derivation ${d_{a,n}}_{n=0}^infty$ such that $D_n(a)=d_{a,n}(a)$ for each non-negative integer $n$. We show that if $mathfrak{A}$ is a $C^*$-algebra t...

Quasicoherent sheaves should be thought of as the scheme-theoretic analogs of vector bundles. This analogy might lead one to think that vector bundles over a scheme X should be locally free OX-modules, but this turns out not to be an abelian category, and the category of quasicoherent sheaves contains the category of locally free OX-modules. There are two different different definitions we coul...

This paper presents a research note on the degree to which strictly incremental derivations (that is derivations which are fully connected at each point in time) are possible in Combinatory Categorial Grammar (CCG). There has been a recent surge of interest in incremental parsing both from the psycholinguistic community in a bid to build psycholinguistically plausible models of language compreh...