Small wonders of the Indian market

Heavy competition in India in almost all product categories, due to diversification by large and medium companies and increased entry of multinationals, has restricted the growth of domestic companies. Previously, large companies enjoyed high profit margins by targeting premium priced products in the upper strata of Indian society. High levels of competition from equally reputed brands have not only decreased the companies' market share but also created price wars, reducing profit margins and limiting market growth. This has motivated companies to consider the lower classes and the rural segments, which they had previously ignored. By targeting these segments with products in small packs at lower price points, companies have experienced great success. At the same time, small packs also pose some challenges for the companies. This paper explains the importance of small packs for market expansion in various product categories within the Indian market, drawing on several examples to support the views of the authors. Copyright © 2004 Henry Stewart Publications.     

Resource-origins of Nonmonotonicity

Formal nonmonotonic systems try to model the phenomenon that common sense reasoners are able to “jump” in their reasoning from assumptions Δ to conclusions C without their being any deductive chain from Δ to C. Such jumps are done by various mechanisms which are strongly dependent on context and knowledge of how the actual world functions. Our aim is to motivate these jump rules as inference rules designed to optimise survival in an environment with scant resources of effort and time. We begin with a general discussion and quickly move to Section 3 where we introduce five resource principles. We show that these principles lead to some well known nonmonotonic systems such as Nute’s defeasible logic. We also give several examples of practical reasoning situations to illustrate our principles. Edited by Hannes Leitgeb     

LÉVY HIERARCHY IN WEAK SET THEORIES

We investigate the interactions of formula complexity in weak set theories with the axioms available there. In particular, we show that swapping bounded and unbounded quantification preserves formula complexity in presence of the axiom of foundation weakened to an arbitrary set base, while it does not if the axiom of foundation is further weakened to a proper class base. More attention is being paid to the necessary axioms employed in the positive results, than to the combinatorial strength of the positive results themselves.     

Propositions, Sets, and Worlds

If we agree with Michael Jubien that propositions do not exist, while accepting the existence of abstract sets in a realist mathematical ontology, then the combined effect of these ontological commitments has surprising implications for the metaphysics of modal logic, the ontology of logically possible worlds, and the controversy over modal realism versus actualism. Logically possible worlds as maximally consistent proposition sets exist if sets generally exist, but are equivalently expressed as maximally consistent conjunctions of the same propositions in corresponding sets. A conjunction of propositions, even if infinite in extent, is nevertheless itself a proposition. If sets and hence proposition sets exist but propositions do not exist, then whether or not modal realism is true depends on which of two apparently equivalent methods of identifying, representing, or characterizing logically possible worlds we choose to adopt. I consider a number of reactions to the problem, concluding that the best solution may be to reject the conventional model set theoretical concept of logically possible worlds as maximally consistent proposition sets, and distinguishing between the actual world alone as maximally consistent and interpreting all nonactual merely logically possible worlds as submaximal. I am grateful to the Netherlands Institute for Advanced Study in the Humanities and Social Sciences (NIAS), Royal Netherlands Academy of Arts and Sciences (KNAW), for supporting this among related research projects in philosophical logic and philosophy of mathematics during my Resident Research Fellowship in 2005-2006.     

MV-Algebras and Quantum Computation

We introduce a generalization of MV algebras motivated by the investigations into the structure of quantum logical gates. After laying down the foundations of the structure theory for such quasi-MV algebras, we show that every quasi-MV algebra is embeddable into the direct product of an MV algebra and a “flat” quasi-MV algebra, and prove a completeness result w.r.t. a standard quasi-MV algebra over the complex numbers. Presented by Heinrich Wansing     

Component Models for Fuzzy Data

The fuzzy perspective in statistical analysis is first illustrated with reference to the “Informational Paradigm” allowing us to deal with different types of uncertainties related to the various informational ingredients (data, model, assumptions). The fuzzy empirical data are then introduced, referring to J LR fuzzy variables as observed on I observation units. Each observation is characterized by its center and its left and right spreads (LR₁ fuzzy number) or by its left and right “centers” and its left and right spreads (LR₂ fuzzy number). Two types of component models for LR₁ and LR₂ fuzzy data are proposed. The estimation of the parameters of these models is based on a Least Squares approach, exploiting an appropriately introduced distance measure for fuzzy data. A simulation study is carried out in order to assess the efficacy of the suggested models as compared with traditional Principal Component Analysis on the centers and with existing methods for fuzzy and interval valued data. An application to real fuzzy data is finally performed. We would like to express our gratitude to the Editor, the Associate Editor, and the Referees whose comments and suggestions improved significantly the quality of the paper.     

Single and double alternation learning in rats: The role of set size and correction

In many experiments, rats have evidenced extreme difficulty mastering alternation patterns. In three experiments, we explored rats’ ability to learn double alternation patterns and possible reasons behind their past difficulties with such patterns. In Experiment 1, rats learned single and double alternation patterns. In the second and third experiment, we explored the role of correction and interference from stimulus set size on rats’ learning of double alternation patterns. Our results showed that rats easily learned both single and double alternation patterns and that stimulus set size had no noticeable effect on learning double alternation patterns. Findings additionally evidenced that correction played an important role in rats’ learning double alternation patterns.     

On Vagueness,Truth Values and Fuzzy Logics

Some aspects of vagueness as presented in Shapiro’s book Vagueness in Context [23] are analyzed from the point of fuzzy logic. Presented are some generalizations of Shapiro’s formal apparatus. Presented by Daniele Mundici     

Another Paradox In Naive Set-Theory

Reasonning in naive set theory (with unlimited comprehension), we derive a paradox (a formal contradiction) which can be seen as a variant of the Burali-Forti paradox. Presented by Robert Goldblatt     

The Buss–Perry Aggression Questionnaire: Some unfinished business

This article gauges the extent to which items and sum scores of the Buss–Perry Aggression Questionnaire (BPAQ) are contaminated with social desirability response set (SDR), and the extent to which that contamination results in biased findings. Special validity coefficients are introduced for that purpose. Although the SDR confound was quite substantial across all items (with one exception), it is argued on the basis of the size of the introduced validity coefficients and other, logical considerations that paradoxically the confound had minimally distorting effects in estimating the BPAQ models selected for probing the extent of bias.