This book explores the results of applying empirical methods to the philosophy of logic and mathematics. Much of the work that has earned experimental philosophy a prominent place in twenty-first century philosophy is concerned with ethics or epistemology. But, as this book shows, empirical methods are just as much at home in logic and the philosophy of mathematics. -/- Chapters demonstrate and discuss the applicability of a wide range of empirical methods including experiments, surveys, interviews, and data-mining. Distinct themes emerge (...) that reflect recent developments in the field, such as issues concerning the logic of conditionals and the role played by visual elements in some mathematical proofs. -/- Featuring leading figures from experimental philosophy and the fields of philosophy of logic and mathematics, this collection reveals that empirical work in these disciplines has been quietly thriving for some time and stresses the importance of collaboration between philosophers and researchers in mathematics education and mathematical cognition. (shrink)

This volume presents the proceedings from the Eleventh Brazilian Logic Conference on Mathematical Logic held by the Brazilian Logic Society in Salvador, Bahia, Brazil. The conference and the volume are dedicated to the memory of professor Mario Tourasse Teixeira, an educator and researcher who contributed to the formation of several generations of Brazilian logicians. Contributions were made from leading Brazilian logicians and their Latin-American and European colleagues. All papers were selected by a careful refereeing processs and were revised and (...) updated by their authors for publication in this volume. There are three sections: Advances in Logic, Advances in Theoretical Computer Science, and Advances in Philosophical Logic. Well-known specialists present original research on several aspects of model theory, proof theory, algebraic logic, category theory, connections between logic and computer science, and topics of philosophical logic of current interest. Topics interweave proof-theoretical, semantical, foundational, and philosophical aspects with algorithmic and algebraic views, offering lively high-level research results. (shrink)

The IOth International Congress of Logic, Methodology and Philosophy of Science, which took place in Florence in August 1995, offered a vivid and comprehensive picture of the present state of research in all directions of Logic and Philosophy of Science. The final program counted 51 invited lectures and around 700 contributed papers, distributed in 15 sections. Following the tradition of previous LMPS-meetings, some authors, whose papers aroused particular interest, were invited to submit their works for publication in a collection (...) of selected contributed papers. Due to the large number of interesting contributions, it was decided to split the collection into two distinct volumes: one covering the areas of Logic, Foundations of Mathematics and Computer Science, the other focusing on the general Philosophy of Science and the Foundations of Physics. As a leading choice criterion for the present volume, we tried to combine papers containing relevant technical results in pure and applied logic with papers devoted to conceptual analyses, deeply rooted in advanced present-day research. After all, we believe this is part of the genuine spirit underlying the whole enterprise of LMPS studies. (shrink)

This volume will be of particular interest to researchers working in the history, and in the philosophy, of logic and mathematics, and more generally, to ...

Undergraduate students with no prior classroom instruction in mathematical logic will benefit from this evenhanded multipart text by one of the centuries greatest authorities on the subject. Part I offers an elementary but thorough overview of mathematical logic of first order. The treatment does not stop with a single method of formulating logic; students receive instruction in a variety of techniques, first learning model theory (truth tables), then Hilbert-type proof theory, and proof theory handled through derived rules. Part (...) II supplements the material covered in Part I and introduces some of the newer ideas and the more profound results of logical research in the twentieth century. Subsequent chapters introduce the study of formal number theory, with surveys of the famous incompleteness and undecidability results of Godel, Church, Turing, and others. The emphasis in the final chapter reverts to logic, with examinations of Godel's completeness theorem, Gentzen's theorem, Skolem's paradox and nonstandard models of arithmetic, and other theorems. Unabridged republication of the edition published by John Wiley & Sons, Inc. New York, 1967. Preface. Bibliography. Theorem and Lemma Numbers: Pages. List of Postulates. Symbols and Notations. Index. (shrink)

Together, Models and Computability and its sister volume Sets and Proofs will provide readers with a comprehensive guide to the current state of mathematical logic. All the authors are leaders in their fields and are drawn from the invited speakers at 'Logic Colloquium '97' (the major international meeting of the Association of Symbolic Logic). It is expected that the breadth and timeliness of these two volumes will prove an invaluable and unique resource for specialists, post-graduate researchers, and the (...) informed and interested nonspecialist. (shrink)

This is an introduction for readers with some basic knowledge of logic to contemporary logical analyses of information flow and multi-agent activity with an emphasis on new perspectives and new research directions. The first major topic are dynamic-epistemic logics for analyzing information dynamics and information update based on new observations, as well as the induced processes of knowledge change and belief revision. The second part of the book connects these dynamic-epistemic logics to richer mathematical models coming from dependence (...) logic, topology and probability. In a third and final part, all these systems are brought to bear on the study of agency in games, bringing together logics for analyzing games and games for analyzing logics in one perspective. An appendix discusses a recent view on how qualitative logical and quantitative arithmetical approaches to reasoning can live together and inform each other. A further appendix summarizes the background in modal logic that is needed for this course. (shrink)

For more than 60 years, Jim Lambek has been a profoundly inspirational mathematician, with groundbreaking contributions to algebra, category theory, linguistics, theoretical physics, logic and proof theory. This Festschrift was put together on the occasion of his 90th birthday. The papers in it give a good picture of the multiple research areas where the impact of Jim Lambek's work can be felt. The volume includes contributions by prominent researchers and by their students, showing how Jim Lambek's ideas keep inspiring (...) upcoming generations of scholars. (shrink)

This English translation of the author's original work has been thoroughly revised, expanded and updated. The book covers logical systems known as type-free or self-referential . These traditionally arise from any discussion on logical and semantical paradoxes. This particular volume, however, is not concerned with paradoxes but with the investigation of type-free sytems to show that: (i) there are rich theories of self-application, involving both operations and truth which can serve as foundations for property theory and formal semantics; (ii) these (...) theories provide a new outlook on classical topics, such as inductive definitions and predicative mathematics; (iii) they are particularly promising with regard to applications. Research arising from paradoxes has moved progressively closer to the mainstream of mathematical logic and has become much more prominent in the last twenty years. A number of significant developments, techniques and results have been discovered. Academics, students and researchers will find that the book contains a thorough overview of all relevant research in this field. (shrink)

This volume presents work that evolved out of the Third Conference on Situation Theory and Its Applications, held at Oiso, Japan, in November of 1991. The chapters presented in this volume continue the mathematical development of situation theory, including the introduction of a graphical notation; and the applications of situation theory discussed are wide-ranging, including topics in natural language semantics and philosophical logic, and exploring the use of information theory in the social sciences. The research presented in this (...) volume reflects a growing international and interdisciplinary activity of importance for many fields concerned with information. (shrink)

Gert H. Müller The growth of the number of publications in almost all scientific areas,· as in the area of (mathematical) logic, is taken as a sign of our scientifically minded culture, but it also has a terrifying aspect. In addition, given the rapidly growing sophistica tion, specialization and hence subdivision of logic, researchers, students and teachers may have a hard time getting an overview ofthe existing literature, partic ularly if they do not have an extensive library available in (...) their neighbourhood: they simply do not even know what to ask for! More specifically, if someone vaguely knows that something vaguely connected with his interests exists some where in the literature, he may not be able to find it even by searching through the publications scattered in the review journals. Answering this challenge was and is the central motivation for compiling this Bibliography. The Bibliography comprises (presently) the following six volumes (listed with the corresponding Editors): I. Classical Logic W. Rautenberg II. Non-c1assical Logics W. Rautenberg IH. Model Theory H. -D. Ebbinghaus IV. Recursion Theory P. G. Hinman V. Set Theory A. R. Blass VI. ProofTheory; Constructive Mathematics J. E. Kister; D. van Dalen & A. S. Troelstra. (shrink)

In recent years, mathematical logic has developed in many directions, the initial unity of its subject matter giving way to a myriad of seemingly unrelated areas. The articles collected here, which range from historical scholarship to recent research in geometric model theory, squarely address this development. These articles also connect to the diverse work of Väänänen, whose ecumenical approach to logic reflects the unity of the discipline.

This book gives a state-of-the-art survey of current research in logic and philosophy of science, as viewed by invited speakers selected by the most prestigious international organization in the field. In particular, it gives a coherent picture of foundational research into the various sciences, both natural and social. In addition, it has special interest items such as symposia on interfaces between logic and methodology, semantics and semiotics, as well as updates on the current state of the field in (...) Eastern Europe and the Far East. (shrink)

Reasoning under uncertainty, that is, making judgements with only partial knowledge, is a major theme in artificial intelligence. Professor Paris provides here an introduction to the mathematical foundations of the subject. It is suited for readers with some knowledge of undergraduate mathematics but is otherwise self-contained, collecting together the key results on the subject, and formalising within a unified framework the main contemporary approaches and assumptions. The author has concentrated on giving clear mathematical formulations, analyses, justifications and consequences (...) of the main theories about uncertain reasoning, so the book can serve as a textbook for beginners or as a starting point for further basic research into the subject. It will be welcomed by graduate students and research workers in logic, philosophy, and computer science as a textbook for beginners, a starting point for further basic research into the subject, and not least, an account of how mathematics and artificial intelligence can complement and enrich each other. (shrink)

Mathematical logic is a branch of mathematics that takes axiom systems and mathematical proofs as its objects of study. This book shows how it can also provide a foundation for the development of information science and technology. The first five chapters systematically present the core topics of classical mathematical logic, including the syntax and models of first-order languages, formal inference systems, computability and representability, and Gödel’s theorems. The last five chapters present extensions and developments of classical (...) class='Hi'>mathematical logic, particularly the concepts of version sequences of formal theories and their limits, the system of revision calculus, proschemes (formal descriptions of proof methods and strategies) and their properties, and the theory of inductive inference. All of these themes contribute to a formal theory of axiomatization and its application to the process of developing information technology and scientific theories. The book also describes the paradigm of three kinds of language environments for theories and it presents the basic properties required of a meta-language environment. Finally, the book brings these themes together by describing a workflow for scientific research in the information era in which formal methods, interactive software and human invention are all used to their advantage. The second edition of the book includes major revisions on the proof of the completeness theorem of the Gentzen system and new contents on the logic of scientific discovery, R-calculus without cut, and the operational semantics of program debugging. This book represents a valuable reference for graduate and undergraduate students and researchers in mathematics, information science and technology, and other relevant areas of natural sciences. Its first five chapters serve as an undergraduate text in mathematical logic and the last five chapters are addressed to graduate students in relevant disciplines. (shrink)

Presents the latest research on how reasoning with analogies, metaphors, metonymies, and images can facilitate mathematical understanding. For math education, educational psychology, and cognitive science scholars.

Vladimir Aleksandrovich Smirnov was born on March 2, 1931. He graduated from Moscow State University in 1954. From 1957 till 1961 he was a lecturer in philosophy and logic at the Tomsk University. Since 1961 his scientific activity continued in Moscow at the Institute of Philosophy of Academy of Sciences of the USSR. From 1970 and till the last days of his life V. A. Smirnov was lecturer and then Professor at the Chair of Logic at Moscow State University. V. (...) A. Smirnov played an important role at the Institute of Philosophy of Russian Academy of Sciences being the Head of Department of Epistemology, Logic and Philosophy of Science and Technology, and the Head of Section of Logic. Last years he was the leader of the Centre of Logical Investigations of Russsian Academy of Sciences. In 1990-91 he founded a new non-goverment Institute of Logic, Cognitive Sciences and Development of Personality for performing research, teaching, editorial and organization activity in the field of humanities. At the Department of Philosophy of Moscow State University and at the Institute of Philosophy V. A. Smirnov and his close colleagues have founded a Russian logical school which brought up many talented researchers who work at several scientific centres in various countries. (shrink)

George Boole (1815-1864) is well known to mathematicians for his research and textbooks on the calculus, but his name has spread world-wide for his innovations in symbolic logic and the development and applications made since his day. The utility of "Boolean algebra" in computing has greatly increased curiosity in the nature and extent of his achievements. His work is most accessible in his two books on logic, "A mathematical analysis of logic" (1947) and "An investigation of the (...) laws of thought" (1954). But at various times he wrote manuscript essays, especially after the publication of the second book; several were intended for a non-technical work, "The Philosophy of logic", which he was not able to complete. This volume contains an edited selection which not only relates them to Boole's publications and the historical context of his time, but also describes their strange history of family, followers and scholars have treid to confect an edition. The book will appeal to logicians, mathematicians and philosophers, and those interested in the histories of the corresponding subjects; and also students of the early Victorian Britain in which they were written. (shrink)

This two-volume work bridges the gap between introductory expositions of logic or set theory on one hand, and the research literature on the other. It can be used as a text in an advanced undergraduate or beginning graduate course in mathematics, computer science, or philosophy. The volumes are written in a user-friendly conversational lecture style that makes them equally effective for self-study or class use. Volume II, on formal (ZFC) set theory, incorporates a self-contained 'chapter 0' on proof techniques (...) so that it is based on formal logic, in the style of Bourbaki. The emphasis on basic techniques will provide the reader with a solid foundation in set theory and provides a context for the presentation of advanced topics such as absoluteness, relative consistency results, two expositions of Godel's constructible universe, numerous ways of viewing recursion, and a chapter on Cohen forcing. (shrink)

This book is devoted to a different proposal--that the logical structure of the scientist's method should guarantee eventual arrival at the truth given the scientist's background assumptions.

Architecture of Mathematics describes the logical structure of Mathematics from its foundations to its real-world applications. It describes the many interweaving relationships between different areas of mathematics and its practical applications, and as such provides unique reading for professional mathematicians and nonmathematicians alike. This book can be a very important resource both for the teaching of mathematics and as a means to outline the research links between different subjects within and beyond the subject. Features All notions and properties are (...) introduced logically and sequentially, to help the reader gradually build understanding. Focusses on illustrative examples that explain the meaning of mathematical objects and their properties. Suitable as a supplementary resource for teaching undergraduate mathematics, and as an aid to interdisciplinary research. Forming the reader's understanding of Mathematics as a unified science, the book helps to increase his general mathematical culture. (shrink)

The Handbook of the Logic of Argument and Inference is an authoritative reference work in a single volume, designed for the attention of senior undergraduates, graduate students and researchers in all the leading research areas concerned with the logic of practical argument and inference. After an introductory chapter, the role of standard logics is surveyed in two chapters. These chapters can serve as a mini-course for interested readers, in deductive and inductive logic, or as a refresher. Then follow two (...) chapters of criticism; one the internal critique and the other the empirical critique. The first deals with objections to standard logics (as theories of argument and inference) arising from the research programme in philosophical logic. The second canvasses criticisms arising from work in cognitive and experimental psychology. The next five chapters deal with developments in dialogue logic, interrogative logic, informal logic, probability logic and artificial intelligence. The last chapter surveys formal approaches to practical reasoning and anticipates possible future developments. Taken as a whole the Handbook is a single-volume indication of the present state of the logic of argument and inference at its conceptual and theoretical best. Future editions will periodically incorporate significant new developments. (shrink)

Dieser Band enthält die vier Arbeiten Freges: Begriffsschrift, eine der arithmetischen nachgebildeten Formelsprache, 1879; Anwendungen der Begriffsschrift, 1879; Über den Briefwechsel Leibnizens und Huggens mit Papin, 1881; Über den Zweck der Begriffsschrift, 1883; Über die wissenschaftliche Berechtigung einer Begriffsschrift, 1882. Frege's research work in the field of mathematical logic is of great importance for the present-day analytic philosophy. We actually owe to Frege a great amount of basical insight and exemplary research, which set up a new standard (...) also in other fields of knowledge. As the founder of mathematical logic he severely examindes the syllogisms on which arithmetic is built up. In doing so, Frege recognized that our colloquial language is inadequate to define logic structures. His notional language corresponded to the artaivicial logical language demandes by Leibniz. Frege's achievement in the field of logic were so important, that they radiated into the domain of philosophy and influenced the development of mathematical logic decisively. (shrink)

This book addresses the logical aspects of the foundations of scientific theories. Even though the relevance of formal methods in the study of scientific theories is now widely recognized and regaining prominence, the issues covered here are still not generally discussed in philosophy of science. The authors focus mainly on the role played by the underlying formal apparatuses employed in the construction of the models of scientific theories, relating the discussion with the so-called semantic approach to scientific theories. The book (...) describes the role played by this metamathematical framework in three main aspects: considerations of formal languages employed to axiomatize scientific theories, the role of the axiomatic method itself, and the way set-theoretical structures, which play the role of the models of theories, are developed. The authors also discuss the differences and philosophical relevance of the two basic ways of aximoatizing a scientific theory, namely Patrick Suppes’ set theoretical predicates and the "da Costa and Chuaqui" approach. This book engages with important discussions of the nature of scientific theories and will be a useful resource for researchers and upper-level students working in philosophy of science. (shrink)

The study of graph structure has advanced in recent years with great strides: finite graphs can be described algebraically, enabling them to be constructed out of more basic elements. Separately the properties of graphs can be studied in a logical language called monadic second-order logic. In this book, these two features of graph structure are brought together for the first time in a presentation that unifies and synthesizes research over the last 25 years. The author not only provides a (...) thorough description of the theory, but also details its applications, on the one hand to the construction of graph algorithms, and, on the other to the extension of formal language theory to finite graphs. Consequently the book will be of interest to graduate students and researchers in graph theory, finite model theory, formal language theory, and complexity theory. (shrink)

An introduction to writing proofs, presented through compelling mathematical statements with interesting elementary proofs. This book offers an introduction to the art and craft of proof-writing. The author, a leading research mathematician, presents a series of engaging and compelling mathematical statements with interesting elementary proofs. These proofs capture a wide range of topics, including number theory, combinatorics, graph theory, the theory of games, geometry, infinity, order theory, and real analysis. The goal is to show students and aspiring (...) mathematicians how to write proofs with elegance and precision. (shrink)

One effect of information technology is the increasing need to present information visually. The trend raises intriguing questions. What is the logical status of reasoning that employs visualization? What are the cognitive advantages and pitfalls of this reasoning? What kinds of tools can be developed to aid in the use of visual representation? This newest volume on the Studies in Logic and Computation series addresses the logical aspects of the visualization of information. The authors of these specially commissioned papers explore (...) the properties of diagrams, charts, and maps, and their use in problem solving and teaching basic reasoning skills. As computers make visual representations more commonplace, it is important for professionals, researchers and students in computer science, philosophy, and logic to develop an understanding of these tools; this book can clarify the relationship between visuals and information. (shrink)

"This book is interesting and well-written. The research methods were explained clearly and conclusions were summarized nicely. It is a relatively quick read at only 130 pages. Anyone who has been told, or who has told others, that mathematicians make better thinkers should read this book." MAA Reviews "The authors particularly attend to protecting positive correlations against the self-selection interpretation, merely that logical minds elect studying more mathematics. Here, one finds a stimulating survey of the systemic difficulties people have (...) with basic syllogisms and deductions." CHOICE connect "The authors particularly attend to protecting positive correlations against the self-selection interpretation, merely that logical minds elect studying more mathematics. Here, one finds a stimulating survey of the systemic difficulties people have with basic syllogisms and deductions." CHOICE Connect For centuries, educational policymakers have believed that studying mathematics is important, in part because it develops general thinking skills that are useful throughout life. This 'Theory of Formal Discipline' (TFD) has been used as a justification for mathematics education globally. Despite this, few empirical studies have directly investigated the issue, and those which have showed mixed results. Does Mathematical Study Develop Logical Thinking? describes a rigorous investigation of the TFD. It reviews the theory's history and prior research on the topic, followed by reports on a series of recent empirical studies. It argues that, contrary to the position held by sceptics, advanced mathematical study does develop certain general thinking skills, however these are much more restricted than those typically claimed by TFD proponents. Perfect for students, researchers and policymakers in education, further education and mathematics, this book provides much needed insight into the theory and practice of the foundations of modern educational policy. (shrink)

Investigating meta-programming within the logic programming paradigm, Meta-Logics and Logic Programming presents original research on an important extension of logic programming that makes it more amenable for knowledge representation and programming in general. The 12 contributions, many written especially for this book, explore the foundations, language design issues, and applications of meta-programming in logic programming. Meta-programming—the process of writing computer programs that can manipulate representations of other programs—has been key both in the foundations of computer science and in its (...) practical developments. Examples of meta-programs include compilers, interpreters, program analyzers, and partial evaluators. The choice of logic programming as a basis for meta-programming offers several practical and theoretical advantages: among them, the possibility of tackling critical foundational problems of meta-programming within a strong theoretical framework, and the surprising ease of programming. The usual framework of logic programming (and more generally first-order logic), however, has to be modified and extended to formally deal with meta-programs, extensions the editors call "meta-logics." Along with an exploration of meta-programming in logic programming, the definitions, formal properties, and use of these extensions constitute one of the book's main themes. The first part of the book, Foundations, focuses on the representation problem—how object programs are represented within meta-programs. The second part, Language Support for Meta-Logics, is concerned with language extensions that make meta-programming easier and more elegant. The third part, Meta-Logics for Knowledge Management, deals with the use of meta-logic for advanced knowledge representation purposes. Logic Programming series. (shrink)

Boston Studies in the Philosophy of Science are devoted to symposia, con gresses, colloquia, monographs and collected papers on the philosophical foundations of the sciences. It is now our pleasure to include A. A. Zi nov'ev's treatise on complex logic among these volumes. Zinov'ev is one of the most creative of modern Soviet logicians, and at the same time an innovative worker on the methodological foundations of science. More over, Zinov'ev, although still a developing scholar, has exerted a sub stantial (...) and stimulating influence upon his colleagues and students in Moscow and within other philosophical and logical circles of the Soviet Union. Hence it may be helpful, in bringing this present work to an English-reading audience, to review briefly some contemporary Soviet investigations into scientific methodology. During the 1950's, a vigorous new research program in logic was under taken, and the initial published work -characteristic of most Soviet pub lications in the logic and methodology of the sciences - was a collection of essays, Logical Investigations (Moscow, 1959). Among the authors, in addition to Zinov'ev himself, were the philosophers A. Kol'man and P. V. Tavanec, and the mathematicians and linguists, S. A. Janovskaja, A. S. Esenin-Vol'pin, S. K. Saumjan, G. N. Povarov. (shrink)

The text considers the impossibility of abstracting away from the sense of formal con­structions in logical and mathematical researches. The validity of the application of the “formal methodology” is allowed only after some system of conventional notations and agreements has been accepted. The context determined by such agreements is called formal. A correlation of constructions and results obtained by formal methods within sev­eral formal contexts is impossible without a consideration of the various semantic aspects of the correlated formal constructions. (...) The author calls such correlations intercontextual. The paper examines two examples of such intercontextual comparisons to demonstrate the necessity of taking into account different semantic components of the compared for­mal constructions. In the context of these conclusions, the author raises the question of the structure and origin of some senses of the “symbols” used in formal constructions and of the “sequences of symbols” constructed from them. The author identifies three main sources of the semantic load carried by formal constructions. Firstly, these are the various aspects of semiotic usage: first of all, the general cultural and general profes­sional semiotic skills of the “interpreter”. Secondly, it is the sense given to formal con­structions by verbal comments, descriptions of the construction process and the associ­ated knowledge of the “interpreter”. Thirdly, these are the senses set by the formal con­structions themselves: at the stage of defining a formal language and at the stage of con­structing a formal deductive or semantic system. The author also considers the fallacy of the assumption of the existence of some universal “global intuition” associated with the very possibility of formal methodology. (shrink)

Language in Action demonstrates the viability of mathematical research into the foundations of categorial grammar, a topic at the border between logic and linguistics. Since its initial publication it has become the classic work in the foundations of categorial grammar. A new introduction to this paperback edition updates the open research problems and records relevant results through pointers to the literature. Van Benthem presents the categorial processing of syntax and semantics as a central component in a more (...) general dynamic logic of information flow, in tune with computational developments in artificial intelligence and cognitive science. Using the paradigm of categorial grammar, he describes the substructural logics driving the dynamics of natural language syntax and semantics. This is a general type-theoretic approach that lends itself easily to proof-theoretic and semantic studies in tandem with standard logic. The emphasis is on a broad landscape of substructural categorial logics and their proof-theoretical and semantic peculiarities. This provides a systematic theory for natural language understanding, admitting of significant mathematical results. Moreover, the theory makes possible dynamic interpretations that view natural languages as programming formalisms for various cognitive activities. (shrink)

Linear Logic is a branch of proof theory which provides refined tools for the study of the computational aspects of proofs. These tools include a duality-based categorical semantics, an intrinsic graphical representation of proofs, the introduction of well-behaved non-commutative logical connectives, and the concepts of polarity and focalisation. These various aspects are illustrated here through introductory tutorials as well as more specialised contributions, with a particular emphasis on applications to computer science: denotational semantics, lambda-calculus, logic programming and concurrency theory. The (...) volume is rounded-off by two invited contributions on new topics rooted in recent developments of linear logic. The book derives from a summer school that was the climax of the EU Training and Mobility of Researchers project 'Linear Logic in Computer Science'. It is an excellent introduction to some of the most active research topics in the area. (shrink)

The new area of logic and computation is now undergoing rapid development. This has affected the social pattern of research in the area. A new topic may rise very quickly with a significant body of research around it. The community, however, cannot wait the traditional two years for a book to appear. This has given greater importance to thematic collections of papers, centred around a topic and addressing it from several points of view, usually as a result of (...) a workshop, summer school, or just a scientific initiative. Such a collection may not be as coherent as a book by one or two authors yet it is more focused than a collection of key papers on a certain topic. It is best thought of as a thematic collection, a study in the area of logic and computation. The new series Studies in Logic and Computation is intended to provide a home for such thematic collections. Substructural logics are nonclassical logics, which arose in response to problems in foundations of mathematics and logic, theoretical computer science, mathematical linguistics, and category theory. They include intuitionistic logic, relevant logic, BCK logic, linear logic, and Lambek's calculus of syntactic categories. Substructural logics differ from classical logics, and from each other, in their presuppositions about Gentzen's structural rules, although their presuppositions about the deductive role of logical constants are invariant. Substructural logics have been a subject of study for logicians during the last sixty years. Specialists have often worked in isolation, however, largely unaware of the contributions of others. This book brings together new papers by some of the most eminent authorities in these varioustraditions to produce a unified view of substructural logics. (shrink)

This book constitutes the refereed proceedings of the 5th Kurt Gödel Colloquium on Computational Logic and Proof Theory, KGC '97, held in Vienna, Austria, in August 1997. The volume presents 20 revised full papers selected from 38 submitted papers. Also included are seven invited contributions by leading experts in the area. The book documents interdisciplinary work done in the area of computer science and mathematical logics by combining research on provability, analysis of proofs, proof search, and complexity.

The present volume stems from a book-proposal made about two years ago to College Publications, London. The main idea was that of illustrating the interplay between the contemporary work in logic and the mainstream mathematics. The division of the volume in two sections - topics in 'logic' vs topics in 'computing' - is more or less conventional. Some contributions are focussed on historical and technical details meant to put in perspective the impact of the work of some outstanding mathematicians and (...) philosophers on the contemporary research in logic and computing science. Some other papers, also with a historical flavour, were supposed to evidentiate punctual methods of research and specific concepts or topics, as, e.g., decidability, computability, randomness, and computational or descriptive complexity. In general, the papers were intended as specific surveys of results. Other volumes - to be issued subsequently in the same series - will hopefully delineate aspects of the contemporary logic landscape that have not been illustrated here. The intended audience of the book includes graduate students in mathematical logic, foundations of matematics, and computing science, as well as philosophers, mathematicians, and, possibly, other scientists interested in the recent research on logic and computing. (shrink)

This is the first volume of a collection of papers in honor of the fiftieth birthday of Jean-Yves Béziau. These 25 papers have been written by internationally distinguished logicians, mathematicians, computer scientists, linguists and philosophers, including Arnon Avron, John Corcoran, Wilfrid Hodges, Laurence Horn, Lloyd Humbertsone, Dale Jacquette, David Makinson, Stephen Read, and Jan Woleński. It is a state-of-the-art source of cutting-edge studies in the new interdisciplinary field of universal logic. The papers touch upon a wide range of topics including (...) combination of logic, non-classical logic, square and other geometrical figures of opposition, categorical logic, set theory, foundation of logic, philosophy and history of logic. This book offers new perspectives and challenges in the study of logic and will be of interest to all students and researchers interested the nature and future of logic. (shrink)

This volume is based on the talks given at the Workshop on Infinity and Truth held at the Institute for Mathematical Sciences, National University of Singapore, from 25 to 29 July 2011. The chapters are by leading experts in mathematical and philosophical logic that examine various aspects of the foundations of mathematics. The theme of the volume focuses on two basic foundational questions: (i) What is the nature of mathematical truth and how does one resolve questions that (...) are formally unsolvable within the Zermelo Fraenkel Set Theory with the Axiom of Choice, and (ii) Do the discoveries in mathematics provide evidence favoring one philosophical view over others? These issues are discussed from the vantage point of recent progresses in foundational studies. The final chapter features questions proposed by the participants of the Workshop that will drive foundational research. The wide range of topics covered here will be of benefit to students, researchers and mathematicians interested in the foundations of mathematics. (shrink)

This proceedings volume contains most of the invited talks presented at the colloquium. The main topics treated are the model theory of arithmetic and algebra, the semantics of natural languages, and applications of mathematical logic to complexity theory. The volume contains both surveys by acknowledged experts and original research papers presenting advances in these disciplines.

"Contains a balanced account of recent advances in set theory, model theory, algebraic logic, and proof theory, originally presented at the Tenth Latin American Symposium on Mathematical Logic held in Bogata, Columbia. Traces new interactions among logic, mathematics, and computer science. Features original research from over 30 well-known experts worldwide.".

Previous research has shown positive relationships between fitness level and different cognitive abilities and academic performance. The purpose of this study was to explore the relationships between logical–mathematical intelligence and mathematical competence with physical fitness in a group of pre-adolescents. Sixty-three children from Castro del Río, aged between 11 and 12 years, participated in this research. The Superior Logical Intelligence Test and the EVAMAT 1.0–5 battery were used. Physical fitness was evaluated by the horizontal jump test, (...) the 4×10 meter speed–agility test, and the Course Navette test. The analyses showed positive relationships between physical fitness with logical–mathematical intelligence and mathematical competence. Specifically, linear regression analyzes indicated that the 4×10 speed–agility test significantly predicted mathematical competence and the horizontal jump test significantly predicted logical–mathematical intelligence. These results are in agreement with previous research, highlighting the importance of improving physical fitness from an early age due to its benefits for intellectual and academic development. (shrink)

A pioneering look at the fundamental role of logic in optimizationand constraint satisfaction While recent efforts to combine optimization and constraintsatisfaction have received considerable attention, little has beensaid about using logic in optimization as the key to unifying thetwo fields. Logic-Based Methods for Optimization develops for thefirst time a comprehensive conceptual framework for integratingoptimization and constraint satisfaction, then goes a step furtherand shows how extending logical inference to optimization allowsfor more powerful as well as flexible modeling and solutiontechniques. Designed to (...) be easily accessible to industryprofessionals and academics in both operations research andartificial intelligence, the book provides a wealth of examples aswell as elegant techniques and modeling frameworks ready forimplementation. Timely, original, and thought-provoking,Logic-Based Methods for Optimization: * Demonstrates the advantages of combining the techniques inproblem solving * Offers tutorials in constraint satisfaction/constraintprogramming and logical inference * Clearly explains such concepts as relaxation, cutting planes,nonserial dynamic programming, and Bender's decomposition * Reviews the necessary technologies for software developersseeking to combine the two techniques * Features extensive references to important computationalstudies * And much more. (shrink)