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.

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.

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)

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)

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 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.

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)

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)

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...

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...

In this paper, we study some classes of logical structures from the universal logic standpoint, viz., those of the Tarski- and the Lindenbaum-types. The characterization theorems for the Tarski- and two of the four different Lindenbaum-type logical structures have been proved as well. The separations between the five classes of logical structures, viz., the four Lindenbaum-types and the Tarski-type have been established via examples. Finally, we study the logical structures that are of both Tarski- and a Lindenbaum-type, show their separations, (...) and end with characterization, adequacy, minimality, and representation theorems for one of the Tarski–Lindenbaum-type logical structures. (shrink)

IntroductionThis paper focuses on a radical feminist engagement with mathematical pluralism. Radical Feminists are interested in a project of methodological re-tooling. Mathematical pluralism appears to be a possible source of help in this direction.Materials and MethodsWith this aim in view the article examines the contributions of Mihir Chakraborty and Amita Chatterjee. By using the method of philosophical argument their theses have been judged from a feminist perspective.ResultsSome very interesing results have been arrived at in terms of accommodating vagueness (...) and pluralism into feminist methodology by the help of mathematical pluralism.DiscussionBy the way of an ongoing discussion the paper states the contours of a radical feminist road map and specifies the kind help they seek from mathematical pluralism. (shrink)

Contributed articles on Indic philosophy, Vedic grammer, and classical Sanskrit literature; includes some on the life of Kr̥ṣṇa Mādho Jha, Sanskrit scholar.

Explanation of terms in Mīmāṃsā, an orthodox school in Hindu philosophy.

Biography of Jiddu Krishnamurti, 1895-1986, Indian philosopher.

Unethical business in India became a recognized phenomenon during the second World War. Academic/journalistic/legal concern with ethics has become visible only during the nineties. Corruption-of-the-poor and corruption-of-the-rich need to be distinguished - especially in the context of globalization. The danger of attributing unethical practices to system failure is recognized. It is also important to bring to bear on intellectual property rights the more fundamental principle of natural property rights. Consciousness ethics will be more crucial than just intellectual ethics.

Neo-Nyaya treatise on verbal testimony, presenting semantic approaches to Sanskrit case and suffix; includes seven Sanskrit commentaries and exhaustive introduction in English.

Treatise with auto-commentary on Dvaita philosophy.

Research work on birth place of Śaṅkarācārya, Hindu philosopher.

Hagiography of Sankaracarya, the exponent of Advaita philosophy.

This omnibus comprises three outstanding books by Professor S.K. Chakraborty on the need for value-driven management and corporate ethics - "Management by Values", "Ethics in Management", and "Values and Ethics for Organizations".

In this work, S.K. Chakraborty develops the themes propounded in his earlier work to provide a systematic presentation of the relevant vedantic and allied principles in a conceptual and empirical framework. From an overall perspective of vedantic ethical vision and its application to managerial and corporate ethical morality, the book examines what the Vedantic ethical system, and great thinkers like Tagore, Gandhi, Burobindo and others, can teach us about such questions as individual leadership, transformation of the work ethos, ethics (...) and productivity, and others. Throughout, the conceptual and the empirical are closely intertwined, and substantial graphic appendices on the Tata leadership crisis of 1991 and the securities scam of 1991-92 give an immediacy and relevance to the analysis. (shrink)

This paper, unveiling the visionary short-sightedness of animal protection, argues for a just vision towards animals in India. Critically analysing the wide range of animal protections in India, the paper finds that in spite of such protections, animals continue to suffer out of unfair and unjust treatments in the country. Considering visionary short-sightedness as the reason behind these unfair and unjust treatments, the paper argues that ensuring the rights of non-human animals to basic capabilities is a fundamental and just vision (...) towards delivering ethical and just actions towards animals. For this, the paper grounds itself on the theoretical foundation of the capabilities approach and makes some policy-level recommendations to protect animals in India. (shrink)

In a world fraught with violence in its macabre form, it is essential to have a broad and clear understanding of the principle of non-violence (ahimsa), its various nuances, its potential and limitations. Covering a span of wisdom literature on the Indian ethos from the times of the Upanishads to the works of modern seers like Gandhi, Tagore and Aurobindo, the author presents the notions of non-violence and violence along a finely graduated scale instead of going into sharp polarities. While (...) making a clear distinction between gross physical violence and the subtle play of violence in words, thoughts and ideas, the paper goes on to offer a critique of modern technology and nuclear proliferation for perpetrating violence on nature and fellow human beings in the name of progress and development. While expressing his admiration for the Gandhian principle of non-violence, the author advocates practical idealism that admits violence with caution but without hatred for the purpose of general welfare (lokasamgraha), along the lines of the messages of Krishna in the Gita. This is of practical necessity till such time as the world has been awakened to a heightened level of spiritual consciousness. (shrink)

The recent revival of interest in the importance of virtues marks a shift of substance and method in thinking about it. The shift is away from discussion of rules and principles and focused on a discussion of traits, character and conditions of their excellence. This article attempts at unfolding the exact nature of an Indian ethics of virtue, which is yet to be explored in a systematic way. This enquiry into the exciting terrain of Indian philosophy inevitably leads to the (...) interesting debate regarding the very possibility of an Indian ethics of virtue. (shrink)

There is a long history to the debate of nationalism. The Indian nationalism has emerged after a long people’s movement the truth to which is often denied by a range of forces who have ideological leanings towards the ideology of Hindutwa. This paper is an attempt to revisit the historical context in which Indian nationalism has emerged and evaluate it in reference to the contemporary time. It emphasizes on the relation between the nation and the state with special reference to (...) its impact on the universities. Further, the paper suggests that in order to uphold the idea of university and nation, an inclusive and secular idea of nation has to be espoused. Lastly, it suggests that a university needs to foster a non sectarian approach and broaden its vision for an internationalist outlook. (shrink)

Discrete Mathematics is designed to serve as a textbook for undergraduate engineering students of computer science and postgraduate students of computer applications. The book would also prove useful to post graduate students of mathematics. It seeks to provide a thorough understanding of the subject and present its practical applications to computer science.

Recent literature shows that ethics of care can be used as a theoretical basis to add a new, important dimension to social issues. Th.

Sanskrit text with autocommentary on Advaita philosophy by Kr̥ṣṇapaṇḍita, 18th century: based on rare manuscripts.