proof theory sequent calculi and related formalisms discrete mathematics and its applications

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Proof Theory

Author : Katalin Bimbo
ISBN : 9781466564664
Genre : Mathematics
File Size : 35. 60 MB
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Although sequent calculi constitute an important category of proof systems, they are not as well known as axiomatic and natural deduction systems. Addressing this deficiency, Proof Theory: Sequent Calculi and Related Formalisms presents a comprehensive treatment of sequent calculi, including a wide range of variations. It focuses on sequent calculi for various non-classical logics, from intuitionistic logic to relevance logic, linear logic, and modal logic. In the first chapters, the author emphasizes classical logic and a variety of different sequent calculi for classical and intuitionistic logics. She then presents other non-classical logics and meta-logical results, including decidability results obtained specifically using sequent calculus formalizations of logics. The book is suitable for a wide audience and can be used in advanced undergraduate or graduate courses. Computer scientists will discover intriguing connections between sequent calculi and resolution as well as between sequent calculi and typed systems. Those interested in the constructive approach will find formalizations of intuitionistic logic and two calculi for linear logic. Mathematicians and philosophers will welcome the treatment of a range of variations on calculi for classical logic. Philosophical logicians will be interested in the calculi for relevance logics while linguists will appreciate the detailed presentation of Lambek calculi and their extensions.

Automated Reasoning With Analytic Tableaux And Related Methods

Author : Renate A. Schmidt
ISBN : 9783319669021
Genre : Computers
File Size : 42. 44 MB
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This book contains the proceedings of the 26th International Conference on Automated Reasoning with Analytics Tableaux and Related Methods, TABLEAUX 2017, held in Brasília, Bazil, in September 2017. The 19 contributed papers presented in this volume were carefully reviewed and selected from 27 submissions.They are organized in topical sections named: Sequent systems; tableaux; transitive closure and cyclic proofs; formalization and complexity. Also included are papers of three invited speakers.

Larisa Maksimova On Implication Interpolation And Definability

Author : Sergei Odintsov
ISBN : 9783319699172
Genre : Philosophy
File Size : 80. 22 MB
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This edited volume focuses on the work of Professor Larisa Maksimova, providing a comprehensive account of her outstanding contributions to different branches of non-classical logic. The book covers themes ranging from rigorous implication, relevance and algebraic logic, to interpolation, definability and recognizability in superintuitionistic and modal logics. It features both her scientific autobiography and original contributions from experts in the field of non-classical logics. Professor Larisa Maksimova's influential work involved combining methods of algebraic and relational semantics. Readers will be able to trace both influences on her work, and the ways in which her work has influenced other logicians. In the historical part of this book, it is possible to trace important milestones in Maksimova’s career. Early on, she developed an algebraic semantics for relevance logics and relational semantics for the logic of entailment. Later, Maksimova discovered that among the continuum of superintuitionisitc logics there are exactly three pretabular logics. She went on to obtain results on the decidability of tabularity and local tabularity problems for superintuitionistic logics and for extensions of S4. Further investigations by Maksimova were aimed at the study of fundamental properties of logical systems (different versions of interpolation and definability, disjunction property, etc.) in big classes of logics, and on decidability and recognizability of such properties. To this end she determined a powerful combination of algebraic and semantic methods, which essentially determine the modern state of investigations in the area, as can be seen in the later chapters of this book authored by leading experts in non-classical logics. These original contributions bring the reader up to date on the very latest work in this field.

J Michael Dunn On Information Based Logics

Author : Katalin Bimbó
ISBN : 9783319293004
Genre : Philosophy
File Size : 56. 46 MB
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This book celebrates and expands on J. Michael Dunn’s work on informational interpretations of logic. Dunn, in his Ph.D. thesis (1966), introduced a semantics for first-degree entailments utilizing the idea that a sentence can provide positive or negative information about a topic, possibly supplying both or neither. He later published a related interpretation of the logic R-mingle, which turned out to be one of the first relational semantics for a relevance logic. An incompatibility relation between information states lends itself to a definition of negation and it has figured into Dunn's comprehensive investigations into representations of various negations. The informational view of semantics is also a prominent theme in Dunn’s research on other logics, such as quantum logic and linear logic, and led to the encompassing theory of generalized Galois logics (or "gaggles"). Dunn’s latest work addresses informational interpretations of the ternary accessibility relation and the very nature of information. The book opens with Dunn’s autobiography, followed by a list of his publications. It then presents a series of papers written by respected logicians working on different aspects of information-based logics. The topics covered include the logic R-mingle, which was introduced by Dunn, and its applications in mathematical reasoning as well as its importance in obtaining results for other relevance logics. There are also interpretations of the accessibility relation in the semantics of relevance and other non-classical logics using different notions of information. It also presents a collection of papers that develop semantics for various logics, including certain modal and many-valued logics. The publication of this book is well timed, since we are living in an "information age.” Providing new technical findings, intellectual history and careful expositions of intriguing ideas, it appeals to a wide audience of scholars and researchers.

Quantitative Graph Theory

Author : Matthias Dehmer
ISBN : 9781466584525
Genre : Computers
File Size : 69. 89 MB
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The first book devoted exclusively to quantitative graph theory, Quantitative Graph Theory: Mathematical Foundations and Applications presents and demonstrates existing and novel methods for analyzing graphs quantitatively. Incorporating interdisciplinary knowledge from graph theory, information theory, measurement theory, and statistical techniques, this book covers a wide range of quantitative-graph theoretical concepts and methods, including those pertaining to real and random graphs such as: Comparative approaches (graph similarity or distance) Graph measures to characterize graphs quantitatively Applications of graph measures in social network analysis and other disciplines Metrical properties of graphs and measures Mathematical properties of quantitative methods or measures in graph theory Network complexity measures and other topological indices Quantitative approaches to graphs using machine learning (e.g., clustering) Graph measures and statistics Information-theoretic methods to analyze graphs quantitatively (e.g., entropy) Through its broad coverage, Quantitative Graph Theory: Mathematical Foundations and Applications fills a gap in the contemporary literature of discrete and applied mathematics, computer science, systems biology, and related disciplines. It is intended for researchers as well as graduate and advanced undergraduate students in the fields of mathematics, computer science, mathematical chemistry, cheminformatics, physics, bioinformatics, and systems biology.

Handbook Of Proof Theory

Author : S.R. Buss
ISBN : 0080533183
Genre : Mathematics
File Size : 43. 2 MB
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This volume contains articles covering a broad spectrum of proof theory, with an emphasis on its mathematical aspects. The articles should not only be interesting to specialists of proof theory, but should also be accessible to a diverse audience, including logicians, mathematicians, computer scientists and philosophers. Many of the central topics of proof theory have been included in a self-contained expository of articles, covered in great detail and depth. The chapters are arranged so that the two introductory articles come first; these are then followed by articles from core classical areas of proof theory; the handbook concludes with articles that deal with topics closely related to computer science.

Proofs And Algorithms

Author : Gilles Dowek
ISBN : 0857291211
Genre : Computers
File Size : 87. 50 MB
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Logic is a branch of philosophy, mathematics and computer science. It studies the required methods to determine whether a statement is true, such as reasoning and computation. Proofs and Algorithms: Introduction to Logic and Computability is an introduction to the fundamental concepts of contemporary logic - those of a proof, a computable function, a model and a set. It presents a series of results, both positive and negative, - Church's undecidability theorem, Gödel’s incompleteness theorem, the theorem asserting the semi-decidability of provability - that have profoundly changed our vision of reasoning, computation, and finally truth itself. Designed for undergraduate students, this book presents all that philosophers, mathematicians and computer scientists should know about logic.

Basic Proof Theory

Author : A. S. Troelstra
ISBN : 0521779111
Genre : Computers
File Size : 87. 36 MB
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Introduction to proof theory and its applications in mathematical logic, theoretical computer science and artificial intelligence.

Lambda Calculus With Types

Author : Henk Barendregt
ISBN : 9780521766142
Genre : Mathematics
File Size : 44. 10 MB
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This handbook with exercises reveals the mathematical beauty of formalisms hitherto mostly used for software and hardware design and verification.

Rethinking India S Oral And Classical Epics

Author : Alf Hiltebeitel
ISBN : 0226340554
Genre : Religion
File Size : 53. 6 MB
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Throughout India and Southeast Asia, ancient classical epics—the Mahabharata and the Ramayana—continue to exert considerable cultural influence. Rethinking India's Oral and Classical Epics offers an unprecedented exploration into South Asia's regional epic traditions. Using his own fieldwork as a starting point, Alf Hiltebeitel analyzes how the oral tradition of the south Indian cult of the goddess Draupadi and five regional martial oral epics compare with one another and tie in with the Sanskrit epics. Drawing on literary theory and cultural studies, he reveals the shared subtexts of the Draupadi cult Mahabharata and the five oral epics, and shows how the traditional plots are twisted and classical characters reshaped to reflect local history and religion. In doing so, Hiltebeitel sheds new light on the intertwining oral traditions of medieval Rajput military culture, Dalits ("former Untouchables"), and Muslims. Breathtaking in scope, this work is indispensable for those seeking a deeper understanding of South Asia's Hindu and Muslim traditions. This work is the third volume in Hiltebeitel's study of the Draupadi cult. Other volumes include Mythologies: From Gingee to Kuruksetra (Volume One), On Hindu Ritual and the Goddess (Volume Two), and Rethinking the Mahabharata (Volume Four).

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