Computation, Logic, Games, and Quantum Foundations - The Many Facets of Samson Abramsky Essays Dedicted to Samson Abramsky on the Occasion of His 60th Birthday
Published in honor of the 60th birthday of Samson Abramsky, this book offers contributions by some of his colleagues, former students and friends, representing his manifold contributions to the disciplines of semantics, logic, games and quantum mechanics.
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| Main Authors | , , |
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| Format | eBook |
| Language | English |
| Published |
Netherlands
Springer Nature
2013
Springer Berlin / Heidelberg Springer |
| Edition | 1 |
| Series | Lecture Notes in Computer Science |
| Subjects | |
| Online Access | Get full text |
| ISBN | 3642381642 9783642381645 3642381634 9783642381638 |
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| Abstract | Published in honor of the 60th birthday of Samson Abramsky, this book offers contributions by some of his colleagues, former students and friends, representing his manifold contributions to the disciplines of semantics, logic, games and quantum mechanics. |
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| AbstractList | This Festschrift volume, published in honor of Samson Abramsky, contains contributions written by some of his colleagues, former students, and friends. In celebration of the 60th birthday of Samson Abramsky, a conference was held in Oxford, UK, during May 28-30, 2010. The papers in this volume represent his manifold contributions to semantics, logic, games, and quantum mechanics. Published in honor of the 60th birthday of Samson Abramsky, this book offers contributions by some of his colleagues, former students and friends, representing his manifold contributions to the disciplines of semantics, logic, games and quantum mechanics. |
| Author | Ong, Luke Panangaden, Prakash Coecke, Bob |
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| Editor | Ong, Luke Panangaden, Prakash Coecke, Bob |
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| Snippet | Published in honor of the 60th birthday of Samson Abramsky, this book offers contributions by some of his colleagues, former students and friends, representing... This Festschrift volume, published in honor of Samson Abramsky, contains contributions written by some of his colleagues, former students, and friends. In... |
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| SubjectTerms | Computer logic Computer programming, programs, data Computer science-Social aspects Game theory |
| Subtitle | Essays Dedicted to Samson Abramsky on the Occasion of His 60th Birthday |
| TableOfContents | 2 A Programing Language for Categories 5.1 Quantization of the Klein-Gordon field -- 5.2 Bosonic Fock Space -- 5.3 Summary -- 6 Quantum Field Theory Abstractly -- 7 Complex Structures and Polarizations -- 7.1 Defining the Vacuum -- 7.2 Bogolioubov Transformations -- 7.3 Rindler Spacetime -- 8 Conclusions -- References -- Bicompletions of Distance Matrices -- 1 Introduction -- 2 Distance Spaces -- 2.1 Definition and Background -- 2.2 Examples -- 2.3 Basic Constructions -- 3 Sequences and Their Limits -- 3.1 Left and Right Sequences -- 3.2 Limits -- 3.3 Weighted Limits -- 3.4 Completions -- 3.5 Adjunctions -- 3.6 Projectors and Nuclei -- 3.7 Cones and Cuts -- 4 Distance Matrices -- 4.1 Definitions -- 4.2 Decomposition through Nucleus -- 5 Bicompletion -- 5.1 Nucleus as a Completion -- 6 Summary and Discussion -- References -- Partial Recursive Functions and Finality -- 1 Introduction -- 2 The Category of Sets and Partial Functions -- 3 Primitive Recursive Functions in Monoidal Categories -- 4 Partial Recursive Functions in Monoidal Categories -- References -- Breaking the Atom with Samson -- 1 Dependence -- 2 Constancy -- 3 Dependence Logic -- 4 DownwardClosure -- 5 Axioms -- 6 Breaking the Atom -- 7 Independence -- 8 Speculation: Breaking the Independence Atom -- References -- Reasoning about Strategies -- 1 Reasoning about Strategies: A Priorip Analysis or Rather Logical Fieldwork? -- 2 The Gale-Stewart Theorem and Its Underlying Temporal Logic of Forcing -- 3 Nondeterminacy, Strategy Stealing, and Temporal Forcing Logics of Special Games -- 4 Explicit Logics of Strategies as Programs -- 5 Zoom, Levels, Invariants, and Definability -- 6 Strategy Logics with Operations on Games -- 7 Knowledge, Preference, and Game Theory -- 8 Conclusion -- References -- Domain Theory in Topical Form -- References -- Kolmogorov Complexity of Categories -- 1 Introduction Intro -- Preface -- Organization -- Table of Contents -- Use of a Canonical Hidden-Variable Space in Quantum Mechanics -- 1 Introduction -- 2 Preliminaries -- 3 TheResult -- References -- Imperfect Information in Logic and Concurrent Games -- 1 Introduction -- 2 Event Structures and Concurrent Games -- 2.1 Concurrent Games and Strategies -- 3 Winning Strategies and Determinacy -- 3.1 Application: Concurrent Games for the Predicate Calculus -- 4 Concurrent Games with Imperfect Information -- 5 Λ-IF: A Parametrized Logic of Independence -- 6 Λ-IF Logic vs. IF Logic -- 6.1 On the Expressivity of Λ-IF -- 7 Conclusion -- References -- Compositional Quantum Logic -- 1 Introduction -- 2 Background -- 3 Abstract Projections -- 4 Quantum Logics for Abstract C*-Algebras -- 5 Composing Quantum Logics -- 6 Commutativity versus Distributivity -- 7 FurtherWork -- References -- The Algebra of Directed Acyclic Graphs -- 1 Introduction -- 2 Directed Acyclic Graphs -- 2.1 Dags -- 2.2 Idags -- 2.3 Operations on Idags -- 2.4 The Category of Finite Abstract Idags -- 3 Product and Permutation Categories -- 3.1 PROPs -- 3.2 Free PROPs -- 4 Examples of Free PROPs -- 4.1 Empty Theory -- 4.2 Nodes -- 4.3 Idempotent Objects -- 4.4 Commutative Monoids and Commutative Comonoids -- 4.5 Commutative Bialgebras -- 4.6 Commutative Hopf Algebras -- 4.7 Commutative Monoids with a Node -- 5 The Algebra of Idags -- 5.1 Algebraic structure -- 5.2 Categorical Interpretation -- 5.3 Compositionality -- 6 Conclusion -- References -- Diagrammatic Reasoning for Delay-Insensitive Asynchronous Circuits -- 1 Asynchronous Circuits -- 1.1 Ebergen's Trace Model -- 2 Preliminaries -- 3 AnAffineModel -- 4 An Interleaved Model -- 4.1 An Idealised Wire Model -- 4.2 A Capacitive Wire Model -- 5 Applications -- 6 Conclusion -- References -- Payoffs, Intensionality and Abstraction in Games 1 Introduction -- 1.1 An Historical Note -- 1.2 This Paper -- 2 The Problem with Payoffs -- 2.1 The Centipede Example -- 2.2 The Prime Factorization Game -- 3 A Common Framework -- 3.1 Turn-Based Probabilistic Games -- 3.2 Game Algebras -- 4 Payoffs in General Game Semantics -- 4.1 Some General Remarks -- 5 Game Theory in Game Semantics -- 5.1 The Centipede PCF Game -- 5.2 The System Administrator Dilemma -- 6 Games and Abstraction -- 6.1 A Simple Example -- 7 FinalRemarks -- References -- On the Theory of Composition in Physics -- 1 Introduction -- 2 Examples and the Tensorial Notation -- 2.1 Tables -- 2.2 Circuits -- 2.3 Other Examples -- 3 Background -- 4 The Description of Composite Objects -- 4.1 The Bipartite Notation and Fundamental Axioms -- 4.2 Tensorial Notation and Composition Locality -- 4.3 Composition Locality and Null Joins -- 4.4 Pruning -- 4.5 Boundaries -- 5 The Composition Principle -- 5.1 Circuits -- 5.2 Labeled Tiles -- 5.3 Other Examples -- 6 Conclusions -- References -- On the Functor 2 -- 1 Introduction -- 2 The Codomain -- 3 TheDomain -- 4 The Functor -- 5 TheImage -- 6 TheFuture -- References -- Quantum Speedup and Categorical Distributivity -- 1 Introduction -- 1.1 Shor's Algorithm: Oracles and Quantum Fourier Transforms -- 1.2 The Aims of this Paper -- 1.3 The Structure of the Paper -- 2 Basic Definitions -- 2.1 Distinguished Objects, and Copying Functors -- 2.2 Copying and the Iterator -- 2.3 String Diagrams for Categories with Distributivity -- 3 Concrete Realisation in Hilbert Space -- 3.1 Interpreting the Direct Sum in the Circuit Model -- 3.2 Controlled Operations and Categorical Swap Maps -- 3.3 Interpreting the Iterator in the Quantum Circuit Paradigm -- 3.4 Applications of the ! -- 4 An Efficient Circuit for the!n(U) Operation -- 4.1 Oracles and Black Boxes -- 5 Conclusions and Future Directions -- References Unifying Semantics for Concurrent Programming -- 1 Introduction -- 2 Denotations -- 2.1 Basic Commands -- 2.2 Sequential Composition -- 2.3 Concurrent Composition -- 2.4 Choice -- 2.5 Galois Inverses -- 2.6 Iteration -- 3 Algebra and Logic -- 3.1 Monotonicity -- 3.2 Sequential Composition -- 3.3 Concurrent Composition -- 3.4 Units -- 3.5 Choice -- 3.6 Galois Adjoints -- 3.7 Iteration -- 4 Conclusion -- References -- Unfixing the Fixpoint: The Theories of the λY -Calculus -- 1 TheλY -Calculus -- 2 λY -Theories -- 2.1 Contextual Characterization of λY -Theories -- 2.2 λ-Theories and λY -Theories -- 2.3 Approximable Theories -- 3 Canonical and Non-canonical Interpretations of Fixpoint Combinators -- 3.1 A Canonical λY -Theory -- 3.2 A Non-canonical λY -Theory -- 4 Final Remarks, Conjectures, Open Problems -- References -- Continuous Domain Theory in Logical Form -- 1 Personal Recollections -- 2 The Handbook Article -- 3 Domain Theory in Logical Form -- 3.1 The Continuous Function Space Construction -- 3.2 The Role of Compactness - First Interpretation -- 3.3 The Role of Compactness - Second Interpretation -- 4 Conclusions -- References -- Presheaf Models of Quantum Computation: An Outline -- 1 Introduction -- 2 Categories of Completely Positive Maps and Superoperators -- 3 Presheaf Models of a Quantum Lambda Calculus -- 3.1 Categorical Models of the Quantum Lambda Calculus -- 3.2 Outline of the Procedure for Obtaining a Concrete Model -- 3.3 Categorical Models of Linear Logic on Presheaf Categories -- 3.4 Idempotent Comonad in the Functor Category -- 3.5 A Strong Comonad -- 3.6 The Functor H : -- 3.7 FT GT Is a Monoidal Adjunction -- 3.8 Abstract Model of the Quantum Lambda Calculus -- 3.9 Towards a Concrete Model: Constructing FinSet Q -- 3.10 A Concrete Model -- 4 Conclusions and Future Work -- References -- Nothing Can Be Fixed -- References Dialogue Categories and Frobenius Monoids -- 1 Frobenius Algebras and 2-Dimensional Cobordism -- 2 Frobenius Pairs -- 3 The Frobenius Bracket -- 4 Helical Frobenius Pairs -- 5 Frobenius Pairs in Ribbon Categories -- 6 Dialogue Categories and Chiralities -- 7 Categorical Bimodules -- 8 Frobenius Pseudomonoids -- 9 Frobenius Amphimonoids -- 10 Epilogue: A Comparison with Day and Street -- 11 Conclusion -- References -- Anatomy of a Domain of Continuous Random Variables II -- 1 Introduction -- 1.1 The Model of Goubault-Larrecq and Varacca -- 1.2 Our Contribution -- 1.3 The Plan of the Paper -- 2 Background -- 2.1 Domains -- 3 On Lawson-Compact Antichains and Thin Probability Measures over A -- 3.1 Lawson-Compact Antichains in A -- 3.2 A Motivating Example -- 3.3 A Bounded Complete Domain of Thin Measures -- 4 Continuous Random Variables -- 4.1 Adding Structure to ΘRVA -- 4.2 Towards a Monad -- 4.3 Relation to the Results of Goubault-Larrecq and Varacca -- 5 Summary and Future Work -- References -- Towards Nominal Abramsky -- 1 Introduction -- 2 RefML -- 3 Game Model -- 4 Groundness -- 5 Innocence -- 6 Conclusion -- References -- Techniques for Formal Modelling and Analysis of Quantum Systems -- 1 Introduction -- 2 Quantum Information Processing -- 2.1 Superposition -- 2.2 Measurement -- 2.3 Operations on a Superposition -- 2.4 No Cloning -- 2.5 Entanglement -- 3 Formal Methods for QIP -- 4 Quantum Teleportation in CQP -- 5 Model-Checking for Quantum Protocols -- 5.1 Quantum Teleportation in QMC -- 5.2 Specifying Properties -- 6 Beyond Stabilizer States: Checking Equivalence -- 7 Conclusion -- References -- Quantum Field Theory for Legspinners -- 1 Introduction -- 2 Geometric Mechanics -- 3 Basic Elements of Quantum Mechanics -- 3.1 Time Evolution -- 3.2 Quantization -- 4 The Harmonic Oscillator -- 5 The Klein-Gordon Field Theory |
| Title | Computation, Logic, Games, and Quantum Foundations - The Many Facets of Samson Abramsky |
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