http://bcpw.bg.pw.edu.pl/Content/1968/Rudiments.pdf

Rudiments of rough sets

http://bcpw.bg.pw.edu.pl/Content/1969/Extensions.pdf

Rough sets: Some extensions

• Constraint domains in which the possible values that a variable can take are restricted to a finite set. • Examples: Boolean constraints, or integer constraints in which each variable is constrained to lie in within a finite range of integers. • Widely used in constraint programming. • Many real problems can be easily represented using constraint domains, e.g.: scheduling, routing and timetabling. • They involve choosing amongst a finite number of possibilities. • Commercial importance to many businesses: e.g. deciding how air crews should be allocated to aircraft flights. • Developed methods by different research communities: Arc and node consistency techniques (artificial intelligence). Bounds propagation techniques (constraint programming). Integer programming (operations research).

/pdf/a-computational-logic-1ahxb2p0nt.pdf

A computational logic

Brian Thompson is a Senior Nutrition Officer at the Food and Agriculture Organization of the United Nations (FAO). FAO is an intergovernmental organization, it has 191 Member Nations, two associate members and one member organization, the European Union. As a knowledge organization, FAO creates and shares critical information about food, agriculture and natural resources in the form of global public goods. FAO plays a connector role, through identifying and working with different partners with established expertise, and facilitating a dialogue between those who have the knowledge and those who need it. By turning knowledge into action, FAO links the field to national, regional and global initiatives in a mutually reinforcing cycle. Its mandate is to raise levels of nutrition and standards of living. What is the size of the malnutrition problem and what regions are most affected? There are persistently high levels of undernutrition. Nearly 870 million people in the world go to bed hungry (1 in 8 people) according to the recently released report of The State of Food Insecurity in the World 2012 (SOFI) and 2 billion have some form of micronutrient malnutrition – this constitutes a crime against humanity and is a responsibility for all of us. Prevalence of undernourishment in developing countries has declined over the past two decades, from 23 to 15 percent. In terms of total numbers in 1990– 92, around 980 million individuals were estimated to be undernourished. The number dropped to 901 million in 1999– 2001, to 885 million in 2006–06 and to 852 million in 2007–09. The financial crisis, economic downturn, persistent food price volatility, drought and other repercussions of climate change since 2006–08 may have prevented any further significant improvements in the number of people who are undernourished in developing countries since then. Africa has by far the highest prevalence, at around 23 percent in 2010–12 but though it is down from what it was in 1990–92 (27 percent) the numbers have risen from 175 million to 239 million with nearly 20 million added in the past four years. In subSaharan Africa, the modest progress achieved in recent years up to 2007 was reversed, with hunger rising 2 percent per year since then. In Asia, both prevalence and numbers dropped over the same period from 24 percent (739 million) to 14 percent (563 million). Latin America and the Caribbean (LAC) boasts the lowest rate of undernourishment (8 percent) among developing country regions but the rate of progress has slowed recently. Countries considered as leastdeveloped countries and lowincome economies have the highest prevalence rates of all around 30 percent but down from the 40 percent levels of twenty years ago.

Interview ラン・ラン

Uncertainty is pervasive in ecology where the difficulties of dealing with sources of uncertainty are exacerbated by variation in the system itself. Attempts at classifying uncertainty in ecology have, for the most part, focused exclusively on epistemic uncertainty. In this paper we classify uncertainty into two main categories: epistemic uncertainty (uncertainty in determinate facts) and linguistic uncertainty (uncertainty in language). We provide a classification of sources of uncertainty under the two main categories and demonstrate how each impacts on applications in ecology and conservation biology. In particular, we demonstrate the importance of recognizing the effect of linguistic uncertainty, in addition to epistemic uncertainty, in ecological applications. The significance to ecology and conservation biology of developing a clear understanding of the various types of uncertainty, how they arise and how they might best be dealt with is highlighted. Finally, we discuss the various general strategies for dealing with each type of uncertainty and offer suggestions for treating compounding uncertainty from a range of sources.

/pdf/a-taxonomy-and-treatment-of-uncertainty-for-ecology-and-1d8ez1odel.pdf

A taxonomy and treatment of uncertainty for ecology and conservation biology

Logic deals with the inevitable - those consequences which follow inescapably from a given set of premisses. This fact has caused it to be seen as different from other more self-questioning branches of philosophy. In this book, Stephen Read sets out to rescue logic from its undeserved reputation as an inflexible, dogmatic discipline by demonstrating that its technicalities and processes are founded on assumptions which are themselves amenable to philosophical investigation. He examines the fundamental principles of consequence, logical truth and correct inference within the context of logic, and shows that the principles by which we delineate consequences are themselves not guaranteed free from error. Central to the notion of truth is the beguiling issue of paradox. Its philosophical value, Read shows, lies in exposing the invalid assumption on which the paradox is built. Thinking About Logic also discusses logical puzzles which introduce questions relating to language, the world, and their relationship. While formal logic often employs its own esoteric language, the achievement of this book is to focus on those issues which raise exciting philosophical questions, and to make them intelligible to readers with no previous knowledge of logic.

Thinking about logic : an introduction to the philosophy of logic

Michael Dummett and Dag Prawitz have argued that a constructivist theory of meaning depends on explicating the meaning of logical constants in terms of the theory of valid inference, imposing a constraint of harmony on acceptable connectives. They argue further that classical logic, in particular, classical negation, breaks these constraints, so that classical negation, if a cogent notion at all, has a meaning going beyond what can be exhibited in its inferential use. I argue that Dummett gives a mistaken elaboration of the notion of harmony, an idea stemming from a remark of Gerhard Gentzen"s. The introduction-rules are autonomous if they are taken fully to specify the meaning of the logical constants, and the rules are harmonious if the elimination-rule draws its conclusion from just the grounds stated in the introduction-rule. The key to harmony in classical logic then lies in strengthening the theory of the conditional so that the positive logic contains the full classical theory of the conditional. This is achieved by allowing parametric formulae in the natural deduction proofs, a form of multiple-conclusion logic.

Harmony and Autonomy in Classical Logic

L'A montre par une formalisation logique pourquoi certains modes syllogistiques sont invalides, ie comment deux premisses vraies peuvent entrainer une conclusion fausse, et soutient que la validite n'est pas purement formelle

Formal and material consequence

From mathematics to philosophy

Inferentialism claims that expressions are meaningful by virtue of rules governing their use. In particular, logical expressions are autonomous if given meaning by their introduction-rules, rules specifying the grounds for assertion of propositions containing them. If the elimination-rules do no more, and no less, than is justified by the introduction-rules, the rules satisfy what Prawitz, following Lorenzen, called an inversion principle. This connection between rules leads to a general form of elimination-rule, and when the rules have this form, they may be said to exhibit "general-elimination" harmony. Ge-harmony ensures that the meaning of a logical expression is clearly visible in its I-rule, and that the I- and E-rules are coherent, in encapsulating the same meaning. However, it does not ensure that the resulting logical system is normalizable, nor that it satisfies the conservative extension property, nor that it is consistent. Thus harmony should not be identified with any of these notions.

/pdf/general-elimination-harmony-and-the-meaning-of-the-logical-2nzw1y3zd0.pdf

Stephen Read

Papers

Thinking about logic : an introduction to the philosophy of logic

Harmony and Autonomy in Classical Logic

Formal and material consequence

From mathematics to philosophy

General-Elimination Harmony and the Meaning of the Logical Constants