Correspondences between Classical, Intuitionistic and Uniform Provability

Based on an analysis of the inference rules used, we provide a characterization of the situations in which classical provability entails intuitionistic provability. We then examine the relationship of these derivability notions to uniform provability, a restriction of intuitionistic provability that embodies a special form of goal-directedness. We determine, first, the circumstances in which the former relations imply the latter. Using this result, we identify the richest versions of the so-called abstract logic programming languages in classical and intuitionistic logic. We then study the reduction of classical and, derivatively, intuitionistic provability to uniform provability via the addition to the assumption set of the negation of the formula to be proved. Our focus here is on understanding the situations in which this reduction is achieved. However, our discussions indicate the structure of a proof procedure based on the reduction, a matter also considered explicitly elsewhere.Comment: 31 page

Reversal of an immunity associated plant cell death program by the growth regulator auxin

One form of plant immunity against pathogens involves a rapid host programmed cell death at the site of infection accompanied by resistance, termed the hypersensitive response (HR). Here it is shown that the HR programmed cell death program initiated by the bacterial type III secretion system dependent proteinaceous elicitor harpin from Erwinia amylovora can be reversed till very late in the process by the plant growth regulator auxin. Early inhibition or late reversal of this cell death program does not affect marker genes tightly correlated with local and systemic resistance. Cross-regulation between cell death programs and growth regulators is prevalent in different kingdoms. Thus, the concept that cell death program can be reversed till late provides a framework for further investigation of such phenomena, in addition to having utility in choosing better targets and strategies for treating mammalian and agricultural diseases

A causal investigation of aggregate output fluctuations in India

This article is an attempt to understand the causal factors behind fluctuations in aggregate output. We find an absence of bidirectional causality between the gross domestic product residual and the gross domestic capital formation residual as well as between the GDP residual and the residual of the combined expenditures of the central and state governments, while the causality between the balance of trade residual and GDP residual is weakly unidirectional.Business Cycles; Hodrick-Prescott filter; Granger Causality;