Two types of logical consequence are compared: one, with respect to matrix and designated elements and the other with respect to ordering in a suitable algebraic structure. Particular emphasis is laid on algebraic structures in which there is no top-element relative to the ordering. The significance of this special condition is discussed. Sequent calculi for a number of such structures are developed. As a consequence it is re-established that the notion of truth as such, not to speak of tautologies, is (...) inessential in order to define validity of an argument. (shrink)

This book introduces the theory of graded consequence and its mathematical formulation. It also compares the notion of graded consequence with other notions of consequence in fuzzy logics, and discusses possible applications of the theory in approximate reasoning and decision-support systems. One of the main points where this book emphasizes on is that GCT maintains the distinction between the three different levels of languages of a logic, namely object language, metalanguage and metametalanguage, and thus avoids the problem of violation of (...) the principle of use and mention; it also shows, gathering evidences from existing fuzzy logics, that the problem of category mistake may arise as a result of not maintaining distinction between levels. (shrink)

Rough Sets were introduced by Z. Pawlak in the year 1982 with the intention to address knowledge representation and data processing from the angle of computation and decision making. The main idea...

Does there exist any equivalence between the notions of inconsistency and consequence in paraconsistent logics as is present in the classical two valued logic? This is the key issue of this paper. Starting with a language where negation ( ${\neg}$ ) is the only connective, two sets of axioms for consequence and inconsistency of paraconsistent logics are presented. During this study two points have come out. The first one is that the notion of inconsistency of paraconsistent logics turns out to (...) be a formula-dependent notion and the second one is that the characterization (i.e. equivalence) appears to be pertinent to a class of paraconsistent logics which have double negation property. (shrink)

This paper contains two traditions of diagrammatic studies namely one, the Euler–Venn–Peirce diagram and the other, following tradition of Aristotle, the square of oppositions. We put together both the traditions to study representations of singular propositions, their negations and the inter relationship between the two. Along with classical negation we have incorporated negation of another kind viz. absence. We have also considered the changes that take place in the context of open universe.

Venn diagram system has been extended by introducing names of individuals and their absence. Absence gives a kind of negation of singular propositions. We have offered here a non-classical interpretation of this negation. Soundness and completeness of the present diagram system have been established with respect to this interpretation.

In this paper, we study two companions of a logic, viz., the left variable inclusion companion and the restricted rules companion, their nature and interrelations, especially in connection with paraconsistency. A sufficient condition for the two companions to coincide has also been proved. Two new logical systems—intuitionistic paraconsistent weak Kleene logic (IPWK) and paraconsistent pre-rough logic (PPRL)—are presented here as examples of logics of left variable inclusion. IPWK is the left variable inclusion companion of intuitionistic propositional logic and is also (...) the restricted rules companion of it. PPRL, on the other hand, is the left variable inclusion companion of pre-rough logic but differs from the restricted rules companion of it. We have discussed algebraic semantics for these logics in terms of Płonka sums. This amounts to introducing a contaminating truth value, intended to denote a state of indeterminacy. (shrink)

The present book discusses all aspects of paraconsistent logic, including the latest findings, and its various systems. It includes papers by leading international researchers, which address the subject in many different ways: development of abstract paraconsistent systems and new theorems about them; studies of the connections between these systems and other non-classical logics, such as non-monotonic, many-valued, relevant, paracomplete and fuzzy logics; philosophical interpretations of these constructions; and applications to other sciences, in particular quantum physics and mathematics. Reasoning with contradictions (...) is the challenge of paraconsistent logic. The book will be of interest to graduate students and researchers working in mathematical logic, computer science, philosophical logic, linguistics and physics. (shrink)

And in this book the distinguished scholar Amartya Sen offers a powerful critique of the theory of social justice that, in its grip on social and political ...

A new diagram system \ where properties are fundamental and an object exists only w.r.t a property is presented. This work modifies both in syntax and semantics the system \ proposed by Choudhury and Chakraborty to picturise and address issues connected with open universe. Semantics for the current system is given. Soundness and completeness w.r.t the semantics are established.

A detailed study of graded frame, graded fuzzy topological system and fuzzy topological space with graded inclusion is already done in our earlier paper. The notions of graded fuzzy topological sys...

Declaring that the universe was created in a certain order, Almighty Allah said, "Do not make mischief on earth after it has been brought into order." With this statement she made, she warned humanity not to disturb the established order. Natural disasters such as epidemics, earthquakes, floods and landslides that we face in the 21st century make it necessary to draw attention to the actions of people once again. Human beings, who interfere with nature irresponsibly, disrupt the balances in the (...) universe, and these disturbed balances return to humanity as a calamity over time. Almighty Allah knows in many verses that these calamities are the result of people's own deeds. To this situation; He emphasizes with the expressions “bimâ kesebû, “bimâ kesebet eydinnâs”, “febimâ kesebet eydiküm”, “bimâ kaddemet eydîhim”,“bimâ zalemû”. It is understood from these expressions that a significant part of the calamities are caused by human error, negligence and unjust interventions. While troubles and calamities mean punishment/retribution for some people, the same event can be a test or a lesson for other people. In this context, it is stated in the Qur'an that many troubles and calamities that have been experienced in the past, such as Noah's Flood, have been made a lesson for all humanity as follows: “As for the people of Noah, We drowned them because they denied their prophet, and made them a sign for the people. We have prepared a painful chastisement for the wrongdoers.” As can be seen, while it is stated in the verse that the cause of the torment is people's denial of the prophets, on the other hand, it is emphasized that this event is a lesson for all humanity. However, it is stated in the next verse that those who do not take lessons from these events and warnings and insist on doing what their souls want deserve punishment. However, the words of the Prophet also guide us regarding the epidemic that befell us and our attitude towards troubles. He (sas) prayed to Allah so that his ummah would not be destroyed altogether. He said that "taun" is a kind of punishment that Allah punishes some people, but it is a mercy for believers. In line with the verses we have mentioned, although most of the calamities are the result of human actions, it is out of the question to call every calamity a divine punishment. Because the prophets suffered the greatest of troubles. This topic is too broad to be tackled from a single point of view. The individual, social, human, divine and test dimensions of the subject should be evaluated as a whole. Therefore, such a sensitive issue that needs to be evaluated from multiple perspectives; Bringing only a part of it to the fore as "trouble equals divine punishment" would be to deviate the subject from its target. In this study, within the framework of the scriptures, the individual, social and divine dimensions of troubles and calamities, these calamities may have spiritual causes as well as material reasons; it will be examined that every calamity is not caused by the mistakes of people, but some of them are caused by what people do. In addition, it will be pointed out that troubles and calamities should be evaluated in a multi-dimensional way within the framework of main elements such as faith, test, hope, precaution, trust, patience, prayer and divine providence. (shrink)

Colloquially, episodic memory is described as “the memory of personally experienced events”. Even though episodic memory has been studied in psychology and neuroscience for about six decades, there is still great uncertainty as to what episodic memory is. Here we ask how episodic memory should be characterized in order to be validated as a natural kind. We propose to conceive of episodic memory as a knowledge-like state that is identified with an experientially based mnemonic representation of an episode that allows (...) for a mnemonic simulation thereof. We call our analysis the Sequence Analysis of Episodic Memory since episodes will be analyzed in terms of sequences of events. Our philosophical analysis of episodic memory is driven and supported by experimental results from psychology and neuroscience. We discuss selected experimental results that provide exemplary evidence for uniform causal mechanisms underlying the properties of episodic memory and argue that episodic memory is a natural kind. The argumentation proceeds along three cornerstones: First, psychological evidence suggests that a violation of any of the proposed conditions for episodic memory amounts to a deficiency of episodic memory and no form of memory or cognitive process but episodic memory fulfills them. Second, empirical results support a claim that the principal anatomical substrate of episodic memory is the hippocampus. Finally, we can pin down causal mechanisms onto neural activities in the hippocampus to explain the psychological states and processes constituting episodic memory. (shrink)

This book develops some of the most important themes of Sen's works over the last decade. He argues in a rich and subtle approach that we should be concerned with people's capabilities rather than their resources or welfare.

Commodities and Capabilities presents a set of inter-related theses concerning the foundations of welfare economics, and in particular about the assessment of personal well-being and advantage. The argument presented focuses on the capability to function, i.e. what a person can do or can be, questioning in the process the more standard emphasis on opulence or on utility. In fact, a person's motivation behind choice is treated here as a parametric variable which may or may not coincide with the pursuit of (...) self-interest. Given the large number of practical problems arising from the roles and limitations of different concepts of interest and the judgement of advantage and well-being, this scholarly investigation is both of theoretical interest and practical import. (shrink)

This book discusses the study and analysis of the physical aspects of social systems and models, inspired by the analogy with familiar models of physical systems and possible applications of statistical physics tools. Unlike the traditional analysis of the physics of macroscopic many-body or condensed matter systems, which is now an established and mature subject, the upsurge in the physical analysis and modelling of social systems, which are clearly many-body dynamical systems, is a recent phenomenon. Though the major developments in (...) sociophysics have taken place only recently, the earliest attempts of proposing "Social Physics" as a discipline are more than one and a half centuries old. Various developments in the mainstream physics of condensed matter systems have inspired and induced the recent growth of sociophysical analysis and models. In spite of the tremendous efforts of many scientists in recent years, the subject is still in its infancy and major challenges are yet to be taken up. An introduction to these challenges is the main motivation for this book. (shrink)

The symposium included in this issue of Analyse & Kritik has provided an excellent occasion to re-examine formal as well as motivational issues underlying the so-called liberal paradox. This rejoinder discusses the significance of the new results and analyses, their bearing on the formulation and implications of rights, and also corrects a misinterpretation. Reflections precipitated by the liberal paradox can influence the acceptability of different principles of social decisions, and also the interpretation of ‘preference’ and ‘unanimity’. They also point to (...) some concerns that are relevant in the formation of individual preferences in a society with interdependent lives. (shrink)

Focuses on the interplay between algorithm design and the underlying computational models.

Based on the 1972 Radcliffe Lectures, this book presents a systematic treatment of the conceptual framework as well as the practical problems of measurement of inequality.

This paper is about three distinct but interrelated problems: (1) the role 0f rights in moral theory, (2) thc characterization 0f agent relative values and their admissibility in consequ<—:ncc—bascd evaluation, and ( 3) the nature 0f moral evaluation 0f states 0f aihirs.

Suitable for students and scholars, this title challenges the assumption that skepticism, rather than established belief, lies at the heart of scientific discovery.

本书内容包括:引言;孔子及《论语》;老子其人与《老子》一书;墨子其人与《墨子》其文;孟子其人和《孟子》其文等。.

Visually impaired people have unique perceptions of and usage requirements for various urban spaces. Therefore, understanding these perceptions can help create reasonable layouts and construct urban infrastructure. This study recruited 26 visually impaired volunteers to evaluate 24 sound environments regarding clarity, comfort, safety, vitality, and depression. This data was collected in seven different types of urban spaces. An independent sample non-parametric test was used to determine the significance of the differences between environmental evaluation results for each evaluation dimension and to (...) summarize the compositions of sound and space elements in the positive and negative influence spaces. The results suggested that visually impaired people feel comfort, safety, and clarity in parks, residential communities, and shopping streets; have negative perceptions of vegetable markets, bus stops, hospitals, and urban departments; feel anxious when traffic sounds, horn sounds, manhole cover sounds, and construction sounds occur; and prefer spaces away from traffic, with fewer and slower vehicles, with a suitable space scale, and moderate crowd density. These results provide a reference for the future design of activity venues and the planning of accessibility systems for visually impaired urban residents. (shrink)