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| Part I Preliminaries 1. Foundations 1.1 Physics without Objects 1.2 Observables 1.3 Finite Dimensional Heuristics 2. Quantum Sets 2.1 Logics and Lattices 2.2 Some First-order Quantum Aggregates 2.2.1 Finite Products 2.2.2 Sequences 2.2.3 Sets 2.2.4 Sibs 2.3 Quantum Set Theory 3. Group Duality, Coherence and Cyclic Actions 3.1 The Duality of Groups and HopfAlgebras 3.1.1 Algebras 3.1.2 Coalgebras 3.1.3 Bialgebras and HopfAlgebras 3.1.4 The Additive Affine Group 3.1.5 Finite Group Algebras 3.1.6 Topological Hopf and Coalgebras 3.1.7 The Algebra of Representative Functions on a Compact Group 3.1.8 Tensor, Symmetric amd Exterior Algebras 3.1.9 The Universal Enveloping Algebra of a Lie Algebra 3.2 Quantum Versions of Cyclic Groups 3.2.1 Quantum Permutations: from (n,C) to Z 3.2.2 Condensation and Coherence 3.2.3 Quantizing Cycles: from 7/n to (n,C) Part II Computational Paradigms 4. Natural Deduction 4.1 Natural Deduction for a Minimal System 4.2 The Curry-Howard Isomorphism 4.3 The Gentzen Sequent Calculus 5. Quantum Logic 5.1 0rthologic and its Model Theory 5.1.1 Orthologic as a Deductive System 5.1.2 Modal Logic and Kripke Models 5.1.3 A Modal Translation Theorem 5.1.4 The Implication Problem and Orthomodular Logic 5.1.5 Orthomodular Foundations for Quantum Mechanics 5.2 Quantum Logic Proper: Hilbert Models 5.2.1 Observables and States for Hilbert Lattices 5.2.2 The Kochen-Specker Theorem a les Isham and Butterfield 5.3 Critique of Quantum Logic 6. The Computational Resources of Quantum Logic 6.1 An Orthological Toy 6.2 GQ: A Minimal Intuitionisitic Propositional Sequent Calculus for Quantum Resources 6.3 Intuitionistic Orthologic and GQ …… Part III The Plenum References Citation Index Notational index and Glossary Subject Index |
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