| Description |
1 online resource (1149 pages : illustrations) |
| Series |
Outstanding contributions to logic ; Volume 25 |
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Outstanding contributions to logic.
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| Contents |
Intro -- Introduction to the Volume -- Contents -- 1 Logical Journeys: A Scientific Autobiography -- 1.1 Beginnings -- 1.2 Domains and Duality (1983-91) -- 1.3 Game Semantics (1992-2000) -- 1.4 Categorical Quantum Mechanics (2001-2009) -- 1.5 Contextuality (2010-Present) -- 1.6 Resources, Game Comonads, and Relating Structure to Power (2017-Present) -- 1.7 Supplements -- 1.8 People -- 1.9 Envoi -- Part I Duality and Domains in Logical Form -- 2 Duality, Intensionality, and Contextuality: Philosophy of Category Theory and the Categorical Unity of Science in Samson Abramsky |
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2.1 Introduction: One-Man Embodiment of Unity of Science -- 2.2 Categorical Foundations and the Unity of Science -- 2.2.1 History and Historiography of Unity and Disunity of Science -- 2.2.2 Categorical Foundations and the Categorical Unity of Science -- 2.2.3 Remarks on the Philosophy of Category Theory -- 2.3 Duality, Intensionality, and Contextuality -- 2.3.1 Duality Between Reality and Observables -- 2.3.2 The Intensional Turn in Logic, Geometry, and Beyond -- 2.3.3 CQM, Reconstructionism, and Lightweight Ontology -- 2.3.4 Contextuality Across the Sciences |
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2.4 Concluding Remarks: Vienna, Stanford, and Oxford -- References -- 3 Minimisation in Logical Form -- 3.1 Introduction -- 3.2 Preliminaries -- 3.2.1 Coalgebras, Algebras and Monads -- 3.2.2 Determinisation -- 3.3 Minimisation via Dual Adjunctions -- 3.3.1 An Illustrative Example -- 3.3.2 Automata, Algebras and Coalgebras -- 3.3.3 Dual Adjunctions of Coalgebras, Algebras and Automata -- 3.3.4 Language Semantics and Trace Logic -- 3.3.5 Reachability and Observability -- 3.3.6 Abstract Minimisation Algorithms -- 3.4 Revisiting Examples -- 3.4.1 Deterministic Kripke Models |
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3.4.2 Weighted Automata -- 3.4.3 Topological Automata via Gelfand Duality -- 3.5 Alternating Automata -- 3.5.1 CABA, EM (N), and Setop -- 3.5.2 Language Acceptance of Alternating Automata -- 3.5.3 Alternating Automata as EM (N)-Automata -- 3.6 Conclusion and Related Work -- References -- 4 A Cook's Tour of Duality in Logic: From Quantifiers, Through Vietoris, to Measures -- 4.1 Algebras from Logic -- 4.2 Topological Methods in Logic -- 4.2.1 Modal Logic and the Vietoris Functor -- 4.2.2 Three Examples of Dual Spaces in Logic -- 4.3 Quantifiers, Free Constructions and Duality |
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4.3.1 Existential Quantification and Vietoris -- 4.3.2 Semiring Quantifiers and Measures -- 4.3.3 Probabilistic Quantifiers and Structural Limits -- 4.4 Outlook -- References -- 5 Stone Duality for Relations -- 5.1 Introduction -- 5.2 Preliminaries on Ordered Category Theory -- 5.2.1 Ordered Categories and Weighted Limits -- 5.2.2 Weakening Relations -- 5.2.3 Ordered Algebra -- 5.2.4 Ordered Stone Duality -- 5.3 The Duality of Spans and Cospans -- 5.3.1 Spans and Cospans -- 5.3.2 Exact Squares -- 5.3.3 Identity and Composition of Spans and Cospans -- 5.4 Dual Relations in Posets |
| Summary |
Samson Abramskys wide-ranging contributions to logical and structural aspects of Computer Science have had a major influence on the field. This book is a rich collection of papers, inspired by and extending Abramskys work. It contains both survey material and new results, organised around six major themes: domains and duality, game semantics, contextuality and quantum computation, comonads and descriptive complexity, categorical and logical semantics, and probabilistic computation. These relate to different stages and aspects of Abramskys work, reflecting its exceptionally broad scope and his ability to illuminate and unify diverse topics. Chapters in the volume include a review of his entire body of work, spanning from philosophical aspects to logic, programming language theory, quantum theory, economics and psychology, and relating it to a theory of unification of sciences using dual adjunctions. The section on game semantics shows how Abramskys work has led to a powerful new paradigm for the semantics of computation. The work on contextuality and categorical quantum mechanics has been highly influential, and provides the foundation for increasingly widely used methods in quantum computing. The work on comonads and descriptive complexity is building bridges between currently disjoint research areas in computer science, relating Structure to Power. The volume also includes a scientific autobiography, and an overview of the contributions. The outstanding set of contributors to this volume, including both senior and early career academics, serve as testament to Samson Abramskys enduring influence. It will provide an invaluable and unique resource for both students and established researchers |
| Bibliography |
Includes bibliographical references |
| Notes |
5.4.1 Extending to Relations via Spans |
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Description based on online resource; title from digital title page (viewed on October 09, 2023) |
| Subject |
Abramsky, Samson, 1953-
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Computer architecture.
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Computer architecture.
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| Form |
Electronic book
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| Author |
Palmigiano, Alessandra, editor
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Sadrzadeh, Mehrnoosh, editor
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| ISBN |
9783031241178 |
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3031241177 |
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