The proceedings volume of the International Conference on Logic, Navya-Nyāya & Applications, held January 3-7, 2007 in Kolkata (Calcutta), India. The Conference aimed to bring together Western/modern logic and traditional Indian systems of logic (especially, the Navya-Nyāya system) with related focus on the work of and in memory of Bimal Krishna Matilal (1935-1991).
Edited in collaboration with FoLLI, the Association of Logic, Language and Information, this book constitutes the 5th volume of the FoLLI LNAI subline. It contains the refereed proceedings of the Third Indian Conference on Logic and Its Applications, ICLA 2009, held in Chennai, India, in January 2009. The 12 revised full papers presented together with 7 invited lectures were carefully reviewed and selected from numerous submissions. The papers present current research in all aspects of formal logic. They address in detail: algebraic logic and set theory, combinatorics and philosophical logic, modal logics with applications to computer science and game theory, and connections between ancient logic systems and modern systems.
Authorship of the great sanskrit language epic poem of India, the Mahabharat, is attributed to the sage krsna Dvaipayana Vyasa. This study focuseson the depictionof vyasa in the Mahabharata, where he is an important character in the tale he is credited, with composing. The interpretation of vyasa is enriched by the different perspectives provided by other literature, including dramas, Jataka tales, Arthasastra, and Puranas.
Illustrations: Numerous B/w Figures Description: Key questions in the history of Navya-nyaya (New Nyaya) remain unresolved: when did this school of logic begin, who was its founder, what distinguishes Navya-nyaya from Pracina-nyaya (Old Nyaya), and so on. This book attempts to answer these key questions in Part I. Part II provides a translation, analysis, and critical edition of the Lion and Tiger Definitions of Invariable Concomitance Chapter (Simha-vyaghra-laksana: LT Chapter) of the Tattva-cintamani-rahasya (TCR) of Mathuranatha (16th-17th c.). The hypothesis adopted by the author with regard to the first question is that Udayana, who lived in the 11th century, is the founder of Navya-nyaya. This hypothesis is closely linked to the hypothesis offered regarding the second question, which is that the feature that distinguishes Navya-nyaya from the earlier school is its description of concepts and the structure of the world in terms of relation. Early Navya-nyaya authors, who flourished between Udayana and Gangesa (14th c.), devised specific terminology, of which delimitor (avacchedaka) and describer (niËpaka) are the most important, in order to identify or specify relation. This book attempts to illustrate the function of these and other Navya-nyaya terms from the viewpoint of relation. The main sources upon which the author has based his conclusions are Udayana s Laksanavali and the chapters on invariable concomitance or pervasion (vyapti) of the Nyaya-siddhanta-dipa (NSD) of Sasadhara (13rd-14th c.), the Tattva-cintamaÆi (TC) of Gangesa, and the TCR. Of these Sanskrit texts no scholar has worked on the Invariable Concomitance Chapter (Vyapti-vada) of the NSD in detail or the LT Chapter of the TCR. The latter chapter follows in the TCR the Five Definitions of Invariable Concomitance Chapter (Vyapti-pancaka), which Ingalls edited, translated, and analyzed in his epoch-making book Materials for the Study of Navya-Nyaya Logic (1951). One major innovation of this book made in Part II is to explain the structure of Navya-nyaya analysis by employing 86 diagrams based on the dharma-dharmin (property and property-possessor) relation, which serve as a visual aid and help readers to more easily understand the complicated structure of its analysis. The diagrams are also helpful in ascertaining how the definitions of invariable concomitance apply to individual cases and how the entities are connected in the application of the definitions. Another major innovation is: almost every sub-section of the LT Chapter of the TCR contains Mathuranatha s clarification of part of the two definitions; but this clarification does not give the definition incorporating prior clarifications and insertions; this book provides such a definition accompanied by a diagram. In other words, Part II illustrates the structure of the whole definition at every process of the clarification, which (definition) is never presented as such in Mathuranatha s text.
Ten essays of this book, two of which are written in Sanskrit, range from modern logic to classical Indian theories of inference. Classical Indian philosophy comprising Pracina and Navya- Nyaya, Sankhya, Buddhist and Jaina logical and philosophical standpoints are discussed in most modern technical terms of western philosophy, often with the aid of terminologies of modern logic. Similarly, western ideas propounded by the ancient Greek philosophers like Aristotle as well as contemporary philosophers such as Frege, Russell, Srawson, Kripke and many others are placed against the backdrop of classical Indian philosophy. The book will be immensely useful to those interested in stimulating meaningful dialogues between philosophical thinkings of India and the West. The book will also be of interest to those who aim at broadening the horizon of logic and philosophy.
This book contains the revised papers presented at the Amsterdam Colloquium 2009, held in Amsterdam, The Netherlands, in December 2009. The 41 thoroughly refereed and revised contributions presented together with the revised abstracts of 5 invited talks are organized in five sections: the first section contains extended abstracts of the talks given by the invited speakers; the second, third and fourth sections contain invited and submitted contributions to the three thematic workshops hosted by the colloquium: the Workshop on Implicature and Grammar, the Workshop on Natural Logic, and the Workshop on Vagueness; the final section consists of submissions to the general program. The topics covered range from descriptive (syntactic and semantic analyses of all kinds of expressions) to theoretical (logical and computational properties of semantic theories, philosophical foundations, evolution and learning of language).
This book provides readers with a snapshot of the state-of-the art in fuzzy logic. Throughout the chapters, key theories developed in the last fifty years as well as important applications to practical problems are presented and discussed from different perspectives, as the authors hail from different disciplines and therefore use fuzzy logic for different purposes. The book aims at showing how fuzzy logic has evolved since the first theory formulation by Lotfi A. Zadeh in his seminal paper on Fuzzy Sets in 1965. Fuzzy theories and implementation grew at an impressive speed and achieved significant results, especially on the applicative side. The study of fuzzy logic and its practice spread all over the world, from Europe to Asia, America and Oceania. The editors believe that, thanks to the drive of young researchers, fuzzy logic will be able to face the challenging goals posed by computing with words. New frontiers of knowledge are waiting to be explored. In order to motivate young people to engage in the future development of fuzzy logic, fuzzy methodologies, fuzzy applications, etc., the editors invited a team of internationally respected experts to write the present collection of papers, which shows the present and future potentials of fuzzy logic from different disciplinary perspectives and personal standpoints.
Since the emergence of the formal concept of probability theory in the seventeenth century, uncertainty has been perceived solely in terms of probability theory. However, this apparently unique link between uncertainty and probability theory has come under investigation a few decades back. Uncertainties are nowadays accepted to be of various kinds. Uncertainty in general could refer to different sense like not certainly known, questionable, problematic, vague, not definite or determined, ambiguous, liable to change, not reliable. In Indian languages, particularly in Sanskrit-based languages, there are other higher levels of uncertainties. It has been shown that several mathematical concepts such as the theory of fuzzy sets, theory of rough sets, evidence theory, possibility theory, theory of complex systems and complex network, theory of fuzzy measures and uncertainty theory can also successfully model uncertainty.
This is a collection of invited papers from the 1975 International Sym posium on Multiple-valued Logic. Also included is an extensive bib liography of works in the field of multiple-valued logic prior to 1975 - this supplements and extends an earlier bibliography of works prior to 1965, by Nicholas Rescher in his book Many-Valued Logic, McGraw-Hill, 1969. There are a number of possible reasons for interest in the present volume. First, the range of various uses covered in this collection of papers may be taken as indicative of a breadth which occurs in the field of multiple-valued logic as a whole - the papers here can do no more than cover a small sample: question-answering systems, analysis of computer hazards, algebraic structures relating to multiple-valued logic, algebra of computer programs, fuzzy sets. Second, a large part of the interest in such uses and applications has occurred in the last twenty, even ten years. It would be too much to expect this to be reflected in Rescher's 1969 book. Third, in the 1970's a series of annual symposia have been held on multiple-valued logic, which have brought much of this into a sharp focus. * The 1971 and 1972 symposia were held at the SUNY at Buffalo, the 1973 symposium at the Uni versity of Toronto, and the 1974 symposium at West Virginia Uni versity. Papers from these symposia are included in the bibliography which may be found in an appendix of this book.
This collection of articles is unique in the way it approaches established material on the various logical traditions in India. Instead of classifying these traditions within Schools as is the usual approach, the material here is classified into sections based on themes ranging from Fundamentals of ancient logical traditions to logic in contemporary mathematics and computer science. This collection offers not only an introduction to the key themes in different logical traditions such as Nyaya, Buddhist and Jaina, it also highlights certain unique characteristics of these traditions as well as contribute new material in the relationship of logic to aesthetics, linguistics, Kashmir Saivism as well as the forgotten Tamil contribution to logic.
