Continuous Lattices and Domains


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Table of contents




Neighborhood Semantics for Modal Logic


Book Description

This book offers a state-of-the-art introduction to the basic techniques and results of neighborhood semantics for modal logic. In addition to presenting the relevant technical background, it highlights both the pitfalls and potential uses of neighborhood models – an interesting class of mathematical structures that were originally introduced to provide a semantics for weak systems of modal logic (the so-called non-normal modal logics). In addition, the book discusses a broad range of topics, including standard modal logic results (i.e., completeness, decidability and definability); bisimulations for neighborhood models and other model-theoretic constructions; comparisons with other semantics for modal logic (e.g., relational models, topological models, plausibility models); neighborhood semantics for first-order modal logic, applications in game theory (coalitional logic and game logic); applications in epistemic logic (logics of evidence and belief); and non-normal modal logics with dynamic modalities. The book can be used as the primary text for seminars on philosophical logic focused on non-normal modal logics; as a supplemental text for courses on modal logic, logic in AI, or philosophical logic (either at the undergraduate or graduate level); or as the primary source for researchers interested in learning about the uses of neighborhood semantics in philosophical logic and game theory.




Handbook of Spatial Logics


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The aim of this handbook is to create, for the first time, a systematic account of the field of spatial logic. The book comprises a general introduction, followed by fourteen chapters by invited authors. Each chapter provides a self-contained overview of its topic, describing the principal results obtained to date, explaining the methods used to obtain them, and listing the most important open problems. Jointly, these contributions constitute a comprehensive survey of this rapidly expanding subject.




Kurt Gödel: Collected Works: Volume III


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"Anyone interested in the life and work of Kurt Gödel, or in the history of mathematical logic in this century, is indebted to all of the contributors to this volume for the care with which they have presented Gödel's work. They have succeeded in using their own expertise to elucidate both the nature and significance of what Gödel and, in turn, mathematical logic have accomplished." --Isis (on volume I). The third volume brings togetherGödels unpublished essays and lectures.




Philosophical Problems in Logic


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The essays in this volume are based on addresses presented during a colloquium on free logic, modal logic and related areas held at the University of California at Irvine, in May of 1968. With the single exception of Dagfinn F011esdal, whose revised address is included in a recent issue of Synthese honoring W. V. Quine, all of the speakers at the Irvine colloquium are contributors to this volume. Thanks are due to Professor A. I. Melden, Chairman of the Department of Philosophy at Irvine, for his enthusiastic support of the colloquium, and to Drs. Gordon Brittan and Daniel Dennett for their help in the administration of the colloquium. Finally. I should also like to thank Professor Ralph W. Gerard, Dean of the Graduate Division of the University of California at Irvine, for the financial support which made the colloquium possible. KAREL LAMBERT Laguna Beach, California, 1969 TABLE OF CONTENTS PREFACE V KAREL LAMBERT and BAS C. VAN FRAASSEN/ Meaning Relations, Possible Objects, and Possible Worlds 1 JAAKKO HINTIKKA / Existential Presuppositions and Uniqueness Presuppositions 20 RICHMOND H. THOMASON / Some Completeness Results for Modal Predicate Calculi 56 H. LEBLANC and R. K. MEYER / Truth-Value Semantics for the Theory of Types 77 J. M. VICKERS / Probability and Non Standard Logics 102 PETER W. WOODRUFF / Logic and Truth Value Gaps 121 DANA SCOTT / Advice on Modal Logic 143 INDEX OF NAMES 175 KAREL LAMBER T AND BAS C.




Category Theory


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Exploring Logical Dynamics


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This book is an exploration of current trends in logical theories of information flow across various fields, such as belief revision in computer science or dynamic semantics in linguistics. It provides one mathematical perspective encompassing all of these. This framework generates a new agenda of questions concerning dynamic inference and dynamic operators. The result is a mathematical theory of process models, simulations between these, and modal languages over them, which is developed in quite some detail. New results include theorems on expressive completeness, representation of styles of inference, and new kinds of decidable remodeling for standard logics. This theory is also confronted with practice in computer science, linguistics and philosophy.




The Coxeter Legacy


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This collection of essays on the legacy of mathematican Donald Coxeter is a mixture of surveys, updates, history, storytelling and personal memories covering both applied and abstract maths. Subjects include: polytopes, Coxeter groups, equivelar polyhedra, Ceva's theorum, and Coxeter and the artists.




General Algebra and Ordered Sets


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