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The Logical Legacy of Nikolai Vasiliev and Modern Logic (Synthese Library #387)

This volume offers a wide range of both reconstructions of Nikolai Vasiliev’s original logical ideas and their implementations in the modern logic and philosophy. A collection of works put together through the international workshop "Nikolai Vasiliev’s Logical Legacy and the Modern Logic," this book also covers foundations of logic in the light of Vasiliev’s contradictory ontology. Chapters range from a look at the Heuristic and Conceptual Background of Vasiliev's Imaginary Logic to Generalized Vasiliev-style Propositions. It includes works which cover Imaginary and Non-Aristotelian Logics, Inconsistent Set Theory and the Expansion of Mathematical Thinking, Plurivalent Logic, and the Impact of Vasiliev's Imaginary Logic on Epistemic Logic. The Russian logician, Vasiliev, was widely recognized as one of the forerunners of modern non-classical logic. His "imaginary logic" developed in some of his work at the beginning of 20th century is often considered to be one of the first systems of paraconsistent and multi-valued logic. The novelty of his logical project has opened up prospects for modern logic as well as for non-classical science in general. This volume contains a selection of papers written by modern specialists in the field and deals with various aspects of Vasiliev's logical ideas. The logical legacy of Nikolai Vasiliev can serve as a promising source for developing an impressive range of philosophical interpretations, as it marries promising technical innovations with challenging philosophical insights.

Logical Methods: The Art of Thinking Abstractly and Mathematically

Many believe mathematics is only about calculations, formulas, numbers, and strange letters. But mathematics is much more than just crunching numbers or manipulating symbols. Mathematics is about discovering patterns, uncovering hidden structures, finding counterexamples, and thinking logically. Mathematics is a way of thinking. It is an activity that is both highly creative and challenging. This book offers an introduction to mathematical reasoning for beginning university or college students, providing a solid foundation for further study in mathematics, computer science, and related disciplines. Written in a manner that directly conveys the sense of excitement and discovery at the heart of doing science, its 25 short and visually appealing chapters cover the basics of set theory, logic, proof methods, combinatorics, graph theory, and much more. In the book you will, among other things, find answers to:What is a proof? What is a counterexample?What does it mean to say that something follows logically from a set of premises?What does it mean to abstract over something?How can knowledge and information be represented and used in calculations?What is the connection between Morse code and Fibonacci numbers?Why could it take billions of years to solve Hanoi's Tower? Logical Methods is especially appropriate for students encountering such concepts for the very first time. Designed to ease the transition to a university or college level study of mathematics or computer science, it also provides an accessible and fascinating gateway to logical thinking for students of all disciplines.

Logical Methods: In Honor of Anil Nerode’s Sixtieth Birthday (Progress in Computer Science and Applied Logic #12)

The twenty-six papers in this volume reflect the wide and still expanding range of Anil Nerode's work. A conference on Logical Methods was held in honor of Nerode's sixtieth birthday (4 June 1992) at the Mathematical Sciences Institute, Cornell University, 1-3 June 1992. Some of the conference papers are here, but others are from students, co-workers and other colleagues. The intention of the conference was to look forward, and to see the directions currently being pursued, in the development of work by, or with, Nerode. Here is a brief summary of the contents of this book. We give a retrospective view of Nerode's work. A number of specific areas are readily discerned: recursive equivalence types, recursive algebra and model theory, the theory of Turing degrees and r.e. sets, polynomial-time computability and computer science. Nerode began with automata theory and has also taken a keen interest in the history of mathematics. All these areas are represented. The one area missing is Nerode's applied mathematical work relating to the environment. Kozen's paper builds on Nerode's early work on automata. Recursive equivalence types are covered by Dekker and Barback, the latter using directly a fundamental metatheorem of Nerode. Recursive algebra is treated by Ge & Richards (group representations). Recursive model theory is the subject of papers by Hird, Moses, and Khoussainov & Dadajanov, while a combinatorial problem in recursive model theory is discussed in Cherlin & Martin's paper. Cenzer presents a paper on recursive dynamics.

Logical Number Theory I: An Introduction (Universitext)

Number theory as studied by the logician is the subject matter of the book. This first volume can stand on its own as a somewhat unorthodox introduction to mathematical logic for undergraduates, dealing with the usual introductory material: recursion theory, first-order logic, completeness, incompleteness, and undecidability. In addition, its second chapter contains the most complete logical discussion of Diophantine Decision Problems available anywhere, taking the reader right up to the frontiers of research (yet remaining accessible to the undergraduate). The first and third chapters also offer greater depth and breadth in logico-arithmetical matters than can be found in existing logic texts. Each chapter contains numerous exercises, historical and other comments aimed at developing the student's perspective on the subject, and a partially annotated bibliography.

Logical Skills: Social-Historical Perspectives (Studies in Universal Logic)

This contributed volume explores the ways logical skills have been perceived over the course of history. The authors approach the topic from the lenses of philosophy, anthropology, sociology, and history to examine two opposing perceptions of logic: the first as an innate human ability and the second as a skill that can be learned and mastered. Chapters focus on the social and political dynamics of the use of logic throughout history, utilizing case studies and critical analyses.Specific topics covered include:the rise of logical skillsproblems concerning medieval notions of idiocy and rationalitydecolonizing natural logicnatural logic and the course of timeLogical Skills: Social-Historical Perspectives will appeal to undergraduate and graduate students, as well as researchers in the fields of history, sociology, philosophy, and logic. Psychology and colonial studies scholars will also find this volume to be of particular interest.

The Logical Structure of Mathematical Physics

This book is about scientific theories of a particular kind - theories of mathematical physics. Examples of such theories are classical and relativis­ tic particle mechanics, classical electrodynamics, classical thermodynamics, statistical mechanics, hydrodynamics, and quantum mechanics. Roughly, these are theories in which a certain mathematical structure is employed to make statements about some fragment of the world. Most of the book is simply an elaboration of this rough characterization of theories of mathematical physics. It is argued that each theory of mathematical physics has associated with it a certain characteristic mathematical struc­ ture. This structure may be used in a variety of ways to make empirical claims about putative applications of the theory. Typically - though not necessarily - the way this structure is used in making such claims requires that certain elements in the structure play essentially different roles. Some playa "theoretical" role; others playa "non-theoretical" role. For example, in classical particle mechanics, mass and force playa theoretical role while position plays a non-theoretical role. Some attention is given to showing how this distinction can be drawn and describing precisely the way in which the theoretical and non-theoretical elements function in the claims of the theory. An attempt is made to say, rather precisely, what a theory of mathematical physics is and how you tell one such theory from anothe- what the identity conditions for these theories are.

Logical Structures for Representation of Knowledge and Uncertainty (Studies in Fuzziness and Soft Computing #14)

It is the business of science not to create laws, but to discover them. We do not originate the constitution of our own minds, greatly as it may be in our power to modify their character. And as the laws of the human intellect do not depend upon our will, so the forms of science, of (1. 1) which they constitute the basis, are in all essential regards independent of individual choice. George Boole [10, p. llJ 1. 1 Comparison with Traditional Logic The logic of this book is a probability logic built on top of a yes-no or 2-valued logic. It is divided into two parts, part I: BP Logic, and part II: M Logic. 'BP' stands for 'Bayes Postulate'. This postulate says that in the absence of knowl­ edge concerning a probability distribution over a universe or space one should assume 1 a uniform distribution. 2 The M logic of part II does not make use of Bayes postulate or of any other postulates or axioms. It relies exclusively on purely deductive reasoning following from the definition of probabilities. The M logic goes an important step further than the BP logic in that it can distinguish between certain types of information supply sentences which have the same representation in the BP logic as well as in traditional first order logic, although they clearly have different meanings (see example 6. 1. 2; also comments to the Paris-Rome problem of eqs. (1. 8), (1. 9) below).

Logical Studies of Paraconsistent Reasoning in Science and Mathematics (Trends in Logic #45)

This book covers work written by leading scholars from different schools within the research area of paraconsistency. The authors critically investigate how contemporary paraconsistent logics can be used to better understand human reasoning in science and mathematics. Offering a variety of perspectives, they shed a new light on the question of whether paraconsistent logics can function as the underlying logics of inconsistent but useful scientific and mathematical theories. The great variety of paraconsistent logics gives rise to various, interrelated questions, such as what are the desiderata a paraconsistent logic should satisfy, is there prospect of a universal approach to paraconsistent reasoning with axiomatic theories, and to what extent is reasoning about sets structurally analogous to reasoning about truth. Furthermore, the authors consider paraconsistent logic’s status as either a normative or descriptive discipline (or one which falls in between) and which inconsistent but non-trivial axiomatic theories are well understood by which types of paraconsistent approaches. This volume addresses such questions from different perspectives in order to (i) obtain a representative overview of the state of the art in the philosophical debate on paraconsistency, (ii) come up with fresh ideas for the future of paraconsistency, and most importantly (iii) provide paraconsistent logic with a stronger philosophical foundation, taking into account the developments within the different schools of paraconsistency.

The Logical Syntax of Greek Mathematics (Sources and Studies in the History of Mathematics and Physical Sciences)

The aim of this monograph is to describe Greek mathematics as a literary product, studying its style from a logico-syntactic point of view and setting parallels with logical and grammatical doctrines developed in antiquity. In this way, major philosophical themes such as the expression of mathematical generality and the selection of criteria of validity for arguments can be treated without anachronism. Thus, the book is of interest for both historians of ancient philosophy and specialists in Ancient Greek, in addition to historians of mathematics.This volume is divided into five parts, ordered in decreasing size of the linguistic units involved. The first part describes the three stylistic codes of Greek mathematics; the second expounds in detail the mechanism of "validation"; the third deals with the status of mathematical objects and the problem of mathematical generality; the fourth analyzes the main features of the "deductive machine," i.e. the suprasentential logical system dictated by the traditional division of a mathematical proposition into enunciation, setting-out, construction, and proof; and the fifth deals with the sentential logical system of a mathematical proposition, with special emphasis on quantification, modalities, and connectors. A number of complementary appendices are included as well. 

A Logical Theory of Nonmonotonic Inference and Belief Change (Artificial Intelligence)

This is the first book that integrates nonmonotonic reasoning and belief change into a single framework from an artificial intelligence logic point-of-view. The approach to both these subjects is based on a powerful notion of an epistemic state that subsumes both existing models for nonmonotonic inference and current models for belief change. Many results and constructions in the book are completely new and have not appeared earlier in the literature.

Logical Thinking in the Pyramidal Schema of Concepts: The Logical and Mathematical Elements

This new volume on logic follows a recognizable format that deals in turn with the topics of mathematical logic, moving from concepts, via definitions and inferences, to theories and axioms. However, this fresh work offers a key innovation in its ‘pyramidal’ graph system for the logical formalization of all these items. The author has developed this new methodology on the basis of original research, traditional logical instruments such as Porphyrian trees, and modern concepts of classification, in which pyramids are the central organizing concept. The pyramidal schema enables both the content of concepts and the relations between the concept positions in the pyramid to be read off from the graph. Logical connectors are analyzed in terms of the direction in which they connect within the pyramid. Additionally, the author shows that logical connectors are of fundamentally different types: only one sort generates propositions with truth values, while the other yields conceptual expressions or complex concepts. On this basis, strong arguments are developed against adopting the non-discriminating connector definitions implicit in Wittgensteinian truth-value tables. Special consideration is given to mathematical connectors so as to illuminate the formation of concepts in the natural sciences. To show what the pyramidal method can contribute to science, a pyramid of the number concepts prevalent in mathematics is constructed. The book also counters the logical dogma of ‘false’ contradictory propositions and sheds new light on the logical characteristics of probable propositions, as well as on syllogistic and other inferences.

Logical Tools for Handling Change in Agent-Based Systems (Cognitive Technologies)

Agents act on the basis of their beliefs and these beliefs change as they interact with other agents. In this book the authors propose and explain general logical tools for handling change. These tools include preferential reasoning, theory revision, and reasoning in inheritance systems, and the authors use these tools to examine nonmonotonic logic, deontic logic, counterfactuals, modal logic, intuitionistic logic, and temporal logic. This book will be of benefit to researchers engaged with artificial intelligence, and in particular agents, multiagent systems and nonmonotonic logic.

The Logical Writings of Karl Popper (Trends in Logic #58)

This open access book is the first ever collection of Karl Popper's writings on deductive logic.Karl R. Popper (1902-1994) was one of the most influential philosophers of the 20th century. His philosophy of science ("falsificationism") and his social and political philosophy ("open society") have been widely discussed way beyond academic philosophy. What is not so well known is that Popper also produced a considerable work on the foundations of deductive logic, most of it published at the end of the 1940s as articles at scattered places. This little-known work deserves to be known better, as it is highly significant for modern proof-theoretic semantics.This collection assembles Popper's published writings on deductive logic in a single volume, together with all reviews of these papers. It also contains a large amount of unpublished material from the Popper Archives, including Popper's correspondence related to deductive logic and manuscripts that were (almost) finished, but did not reach the publication stage. All of these items are critically edited with additional comments by the editors. A general introduction puts Popper's work into the context of current discussions on the foundations of logic. This book should be of interest to logicians, philosophers, and anybody concerned with Popper's work.

The Logician and the Engineer: How George Boole and Claude Shannon Created the Information Age

Boolean algebra, also called Boolean logic, is at the heart of the electronic circuitry in everything we use—from our computers and cars, to home appliances. How did a system of mathematics established in the Victorian era become the basis for such incredible technological achievements a century later? In The Logician and the Engineer, Paul Nahin combines engaging problems and a colorful historical narrative to tell the remarkable story of how two men in different eras—mathematician and philosopher George Boole and electrical engineer and pioneering information theorist Claude Shannon—advanced Boolean logic and became founding fathers of the electronic communications age. Nahin takes readers from fundamental concepts to a deeper and more sophisticated understanding of modern digital machines, in order to explore computing and its possible limitations in the twenty-first century and beyond.

The Logician and the Engineer: How George Boole and Claude Shannon Created the Information Age

Boolean algebra, also called Boolean logic, is at the heart of the electronic circuitry in everything we use—from our computers and cars, to home appliances. How did a system of mathematics established in the Victorian era become the basis for such incredible technological achievements a century later? In The Logician and the Engineer, Paul Nahin combines engaging problems and a colorful historical narrative to tell the remarkable story of how two men in different eras—mathematician and philosopher George Boole and electrical engineer and pioneering information theorist Claude Shannon—advanced Boolean logic and became founding fathers of the electronic communications age. Nahin takes readers from fundamental concepts to a deeper and more sophisticated understanding of modern digital machines, in order to explore computing and its possible limitations in the twenty-first century and beyond.

Logicism, Intuitionism, and Formalism: What Has Become of Them? (Synthese Library #341)

Logicomix: An epic search for truth

This exceptional graphic novel recounts the spiritual odyssey of philosopher Bertrand Russell. In his agonized search for absolute truth, Russell crosses paths with legendary thinkers like Gottlob Frege, David Hilbert, and Kurt Gödel, and finds a passionate student in the great Ludwig Wittgenstein. But his most ambitious goal-to establish unshakable logical foundations of mathematics-continues to loom before him. Through love and hate, peace and war, Russell persists in the dogged mission that threatens to claim both his career and his personal happiness, finally driving him to the brink of insanity. This story is at the same time a historical novel and an accessible explication of some of the biggest ideas of mathematics and modern philosophy. With rich characterizations and expressive, atmospheric artwork, the book spins the pursuit of these ideas into a highly satisfying tale. Probing and ingeniously layered, the book throws light on Russell's inner struggles while setting them in the context of the timeless questions he spent his life trying to answer. At its heart, Logicomix is a story about the conflict between an ideal rationality and the unchanging, flawed fabric of reality.

Logics and Type Systems in Theory and Practice: Essays Dedicated to Herman Geuvers on The Occasion of His 60th Birthday (Lecture Notes in Computer Science #14560)

This Festschrift, dedicated to Herman Geuvers on the occasion of his 60th birthday, contains papers written by many of his closest collaborators. Herman Geuvers is a full professor at Radboud University Nijmegen and holds a part-time professorship at Eindhoven University of Technology. He received his PhD from Radboud University in 1993 and he was promoted to full professor in Computer Assisted Reasoning in 2006. Prof. Geuvers is an internationally renowned researcher in the field of proof assistants, logic in computer science, lambda calculus, and type theory. He has been a steering committee chair of the TYPES and FSCD conferences, chair of related EU Cost Action projects, and program chair or editor of related conferences and special issues in the area of computer science logic. He is a successful, generous and inspiring advisor and educator. He has been director of education and director of research of the Computer Science Institute at Radboud University Nijmegen, and he is currently chair of the examination board of computer science and chair of the board of the Institute for Programming Research and Algorithmics, a Dutch national inter-university research school. The contributions in this volume reflect Prof. Geuvers’ main research interests.

Logics for Computer Science: Classical And Non-classical

Providing an in-depth introduction to fundamental classical and non-classical logics, this textbook offers a comprehensive survey of logics for computer scientists. Logics for Computer Science contains intuitive introductory chapters explaining the need for logical investigations, motivations for different types of logics and some of their history. They are followed by strict formal approach chapters. All chapters contain many detailed examples explaining each of the introduced notions and definitions, well chosen sets of exercises with carefully written solutions, and sets of homework. While many logic books are available, they were written by logicians for logicians, not for computer scientists. They usually choose one particular way of presenting the material and use a specialized language. Logics for Computer Science discusses Gentzen as well as Hilbert formalizations, first order theories, the Hilbert Program, Godel's first and second incompleteness theorems and their proofs. It also introduces and discusses some many valued logics, modal logics and introduces algebraic models for classical, intuitionistic, and modal S4 and S5 logics.The theory of computation is based on concepts defined by logicians and mathematicians. Logic plays a fundamental role in computer science, and this book explains the basic theorems, as well as different techniques of proving them in classical and some non-classical logics. Important applications derived from concepts of logic for computer technology include Artificial Intelligence and Software Engineering. In addition to Computer Science, this book may also find an audience in mathematics and philosophy courses, and some of the chapters are also useful for a course in Artificial Intelligence.

Logics for Emerging Applications of Databases

In this era of heterogeneous and distributed data sources, ranging from semistructured documents to knowledge about coordination processes or workflows, logic provides a rich set of tools and techniques with which to address the questions of how to represent, query and reason about complex data. This book provides a state-of-the-art overview of research on the application of logic-based methods to information systems, covering highly topical and emerging fields: XML programming and querying, intelligent agents, workflow modeling and verification, data integration, temporal and dynamic information, data mining, authorization, and security. It provides both scientists and graduate students with a wealth of material and references for their own research and education.

Logics in Artificial Intelligence: 9th European Conference, JELIA 2004, Lisbon, Portugal, September 27-30, 2004, Proceedings (Lecture Notes in Computer Science #3229)

Logics in Artificial Intelligence: 16th European Conference, JELIA 2019, Rende, Italy, May 7–11, 2019, Proceedings (Lecture Notes in Computer Science #11468)

This book constitutes the proceedings of the 16th European Conference on Logics in Artificial Intelligence, JELIA 2019, held in Rende, Italy, in May 2019. The 50 full papers and 10 short papers included in this volume were carefully reviewed and selected from 101 submissions. Additionally, the book contains 3 invited papers. The accepted papers span a number of areas within Logics in AI, including: belief revision and argumentation; causal, defeasible and inductive reasoning; conditional, probabilistic and propositional logic; description logics; logic programming; modal and default logic; and temporal logic.

Logics in Artificial Intelligence: European Workshop, JELIA ’98 Dagstuhl, Germany, October 12–15, 1998 Proceedings (Lecture Notes in Computer Science #1489)

This volume contains the papers selected for presentation at the conference and two abstracts from invited speakers. The programme committee selected these 25 papers from 12 countries out of 65 submissions from 17 countries. The rst JELIA meeting was in Rosco , France, ten years ago. Afterwards, it took place in the Netherlands, Germany, United Kingdom, Portugal, and now again in Germany. The proceedings of the last four meetings appeared in the Springer-Verlag LNCS series, and a selected series of papers of the English and the Portuguese meeting appeared as special issues in the Journal of Applied Non-Classical Logics and in the Journal of Automated Reasoning, respectively. The aim of JELIA was and still is to provide a forum for the exchange of ideas and results in the domain of foundations of AI, focusing on rigorous descriptions of some aspects of intelligence. These descriptions are promoted by applications, and produced by logical tools and methods. The papers contained in this volume cover the following topics: 1. Logic programming 2. Epistemic logics 3. Theorem proving 4. Non-monotonic reasoning 5. Non-standard logics 6. Knowledge representation 7. Higher order logics We would like to warmly thank the authors, the invited speakers, the m- bers of the program committee, and the additional reviewers listed below. They all have made these proceedings possible and ensured their quality.

Logics in Artificial Intelligence: 13th European Conference, JELIA 2012, Toulouse, France, September 26-28, 2012, Proceedings (Lecture Notes in Computer Science #7519)

This book constitutes the refereed proceedings of the 13th European Conference on Logics in Artificial Intelligence, held in Toulouse, France, in September 2012. The book includes 3 invited talks, 36 regular papers, and 5 system descriptions, selected from 107 submissions. The papers cover various aspects of theory and methods of logic for artificial intelligence.

Logics in Artificial Intelligence: 17th European Conference, JELIA 2021, Virtual Event, May 17–20, 2021, Proceedings (Lecture Notes in Computer Science #12678)

This book constitutes the proceedings of the 17th European Conference on Logics in Artificial Intelligence, JELIA 2021, held as a virtual event, in May 2021. The 27 full papers and 3 short papers included in this volume were carefully reviewed and selected from 68 submissions. The accepted papers span a number of areas within Logics in AI, including: argumentation; belief revision; reasoning about actions, causality, and change; constraint satisfaction; description logics and ontological reasoning; non-classical logics; and logic programming (answer set programming).