Empty Logic

“Covers the basic philosophy and arguments of Mādhyamika, as well as discussing its possible influence on other forms of Buddhist thought, including Zen.”—Journal of Chinese Philosophy The chief purpose of Empty Logic is to expound the Mādhyamika philosophy of emptiness as presented in Chinese sources and to clarify misconceptions about this important Buddhist ideology. It is an attempt to present the earlier Chinese San-lun exposition of Nāgārjuna’s thought. To followers of Mādhyamika, the doctrine of emptiness is not a metaphysical theory; rather it is essentially a way of salvation. Few people know that one of the most significant outcomes of Nāgārjuna’s teaching was the creation of Zen (Ch’an) Buddhism in China. In this work, Hsueh-li Cheng provides a general background of Buddhism to give a historical perspective of Mādhyamika thought and development. After exploring the various meanings and use of emptiness in the process of salvation and illustrating the relationship between Mādhyamika and Zen, Cheng investigates how Mādhyamikas addresses the concepts of reality, God, and knowledge. There follows a brief comparison between Nāgārjuna’s, Kant’s, and Wittgenstein’s philosophies to suggest the unique nature of Nāgārjuna’s teaching and explain why his beliefs cannot be classified alongside the other two thinkers. Teaching emptiness as the middle way, the revolutionary Mādhyamika branch of Buddhism offers a singular and fascinating path to achieving liberation from the evil and suffering of the world.

Free logic - i.e., logic free of existential presuppositions in general and with respect to singular terms in particular- began to come into its own as a field of research in the 1950s. As is the case with so many developments in Western philosophy, its roots can be traced back to ancient Greek philo sophy. It is only during the last fifty years, however, that it has become well established as a branch of modern logic. The name of Karel Lambert is most closely connected with this development: he gave it its name and its profile as a well defined field of research. After a development of fifty years, it is time to look back and take stock while at the same time scanning for new perspectives. This is the purpose of the papers collected in this volume. The first paper is written by Karel Lambert himself who also comments on all the papers of the other authors. In an introductory essay we give a survey of the present status of and new directions in free logic.

What Is Modal Logic Statements regarding necessity and possibility can be represented with the use of a type of logic known as modal logic. As a method for gaining a grasp of ideas like knowledge, obligation, and causality, it is an essential component of philosophy and other subjects that are closely related to it. For instance, the formula can be used to describe the statement that is known in the epistemic modal logic. Using the same formula, one can express that which is a moral responsibility within the framework of deontic modal logic. The conclusions that can be drawn from modal assertions are taken into consideration by modal logic. For instance, the majority of epistemic logics consider the formula to be a tautology, which is a representation of the concept that the only assertions that may be considered to have knowledge are those that are true. How You Will Benefit (I) Insights, and validations about the following topics: Chapter 1: Modal Logic Chapter 2: First-order Logic Chapter 3: Propositional Calculus Chapter 4: Saul Kripke Chapter 5: Kripke Semantics Chapter 6: Temporal Logic Chapter 7: Epistemic Modal Logic Chapter 8: Accessibility Relation Chapter 9: S5 (Modal Logic) Chapter 10: Dynamic Logic (Modal Logic) (II) Answering the public top questions about modal logic. (III) Real world examples for the usage of modal logic in many fields. (IV) 17 appendices to explain, briefly, 266 emerging technologies in each industry to have 360-degree full understanding of modal logic' technologies. Who This Book Is For Professionals, undergraduate and graduate students, enthusiasts, hobbyists, and those who want to go beyond basic knowledge or information for any kind of modal logic.

What Is Inductive Logic Programming A subfield of symbolic artificial intelligence known as inductive logic programming (ILP) use logic programming as a consistent representation for examples, background knowledge, and hypotheses. An ILP system will develop a hypothesised logic program in the event that it is provided with an encoding of the known background knowledge and a collection of examples that are represented as a logical database of facts. This program will involve all of the positive examples and none of the negative instances.In this model, the hypothesis is derived from positive instances, negative examples, and background knowledge. How You Will Benefit (I) Insights, and validations about the following topics: Chapter 1: Inductive Logic Programming Chapter 2: Stephen Muggleton Chapter 3: Progol Chapter 4: Program Synthesis Chapter 5: Inductive Programming Chapter 6: First-Order Logic Chapter 7: List of Rules of Inference Chapter 8: Disjunctive Normal Form Chapter 9: Resolution (Logic) Chapter 10: Answer Set Programming (II) Answering the public top questions about inductive logic programming. (III) Real world examples for the usage of inductive logic programming in many fields. (IV) 17 appendices to explain, briefly, 266 emerging technologies in each industry to have 360-degree full understanding of inductive logic programming' technologies. Who This Book Is For Professionals, undergraduate and graduate students, enthusiasts, hobbyists, and those who want to go beyond basic knowledge or information for any kind of inductive logic programming.

The Lvov-Warsaw School was active in all spheres of philosophy. Its members worked in the border area between philosophy and disci plines such as psychology, linguistics, and literary theory. But its most important achievements were without doubt in logic and philosophical analysis based on logic. The present book is concerned with fields to which the Lvov-Warsaw School made its most important and famous contributions. Data on the School as a whole are included only in the first and last part of the book. This work is based on my monograph (1985), which appeared in Polish. But it is not merely a translation, because some fragments of the Polish version have been omitted (e. g., the chapter on ethics), and some have been revised. Many persons helped me in my work on the book in Polish as well as on the present edition. I must first mention the late Izydora D~mbska, to whom this book is dedicated. On various detailed issues I have availed myself of advice and information given to me by Stefan Amsterdamski, Zdzislaw Augustynek, Kazimierz Czarnota, Henryk Hii, Boleslaw Iwanus, Jacek Jadacki, Jacek KabziIiski, Stanislaw Kiczuk, Tomasz Komendzinski, Janina Kotarbinska, Czeslaw Lejewski, Jerzy Perzanowski, Marian Przet~cki, the late Jerzy Slupecki, Klemens Szaniawski, Stefan Zamecki, Zbigniew Zwinogrodzki i Jan Zygmunt. I am indebted to Jaakko Hintikka for suggesting that my book be trans lated into English and published by Reidel. Olgierd Wojtasiewicz helped me to prepare the English text.

Alex Oliver and Timothy Smiley provide a natural point of entry to what for most readers will be a new subject. Plural logic deals with plural terms ('Whitehead and Russell', 'Henry VIII's wives', 'the real numbers', 'the square root of -1', 'they'), plural predicates ('surrounded the fort', 'are prime', 'are consistent', 'imply'), and plural quantification ('some things', 'any things'). Current logic is singularist: its terms stand for at most one thing. By contrast, the foundational thesis of this book is that a particular term may legitimately stand for several things at once; in other words, there is such a thing as genuinely plural denotation. The authors argue that plural phenomena need to be taken seriously and that the only viable response is to adopt a plural logic, a logic based on plural denotation. They expound a framework of ideas that includes the distinction between distributive and collective predicates, the theory of plural descriptions, multivalued functions, and lists. A formal system of plural logic is presented in three stages, before being applied to Cantorian set theory as an illustration. Technicalities have been kept to a minimum, and anyone who is familiar with the classical predicate calculus should be able to follow it. The authors' approach is an attractive blend of no-nonsense argumentative directness and open-minded liberalism, and they convey the exciting and unexpected richness of their subject. Mathematicians and linguists, as well as logicians and philosophers, will find surprises in this book. This second edition includes a greatly expanded treatment of the paradigm empty term zilch, a much strengthened treatment of Cantorian set theory, and a new chapter on higher-level plural logic.

The A to Z of Logic introduces the central concepts of the field in a series of brief, non-technical, cross-referenced dictionary entries. The 352 alphabetically arranged entries give a clear, basic introduction to a very broad range of logical topics. Entries can be found on deductive systems, such as propositional logic, modal logic, deontic logic, temporal logic, set theory, many-valued logic, mereology, and paraconsistent logic. Similarly, there are entries on topics relating to those previously mentioned such as negation, conditionals, truth tables, and proofs. Historical periods and figures are also covered, including ancient logic, medieval logic, Buddhist logic, Aristotle, Ockham, Boole, Frege, Russell, Gödel, and Quine. There are even entries relating logic to other areas and topics, like biology, computers, ethics, gender, God, psychology, metaphysics, abstract entities, algorithms, the ad hominem fallacy, inductive logic, informal logic, the liar paradox, metalogic, philosophy of logic, and software for learning logic. In addition to the dictionary, there is a substantial chronology listing the main events in the history of logic, an introduction that sketches the central ideas of logic and how it has evolved into what it is today, and an extensive bibliography of related readings. This book is not only useful for specialists but also understandable to students and other beginners in the field.

Edited in collaboration with FoLLI, this book constitutes the refereed proceedings of the 10th Indian Conference on Logic and Its Applications, ICLA 2023, which was held in Indore, India, in March 2023. Besides 6 invited papers presented in this volume, there are 9 contributed full papers which were carefully reviewed and selected from 18 submissions. The volume covers a wide range of topics. These topics are related to modal and temporal logics, intuitionistic connexive and imperative logics, systems for reasoning with vagueness and rough concepts, topological quasi-Boolean logic and quasi-Boolean based rough set models, and first-order definability of path functions of graphs.