Offers a self-contained work presenting basic ideas, classical results, current state of the art and possible future directions in proof complexity.Hinweis: Dieser Artikel kann nur an eine deutsche Lieferadresse ausgeliefert werden.
Jan Krají¿ek is Professor of Mathematical Logic in the Faculty of Mathematics and Physics at Charles University, Prague. He is a member of the Academia Europaea and of the Learned Society of the Czech Republic. He has been an invited speaker at the European Congress of Mathematicians and at the International Congresses of Logic, Methodology and Philosophy of Science.
Inhaltsangabe
Introduction Part I. Basic Concepts: 1. Concepts and problems 2. Frege systems 3. Sequent calculus 4. Quantified propositional calculus 5. Resolution 6. Algebraic and geometric proof systems 7. Further proof systems Part II. Upper Bounds: 8. Basic example of the correspondence between theories and proof systems 9. Two worlds of bounded arithmetic 10. Up to EF via the translation 11. Examples of upper bounds and p-simulations 12. Beyond EF via the ... translation Part III. Lower Bounds: 13. R and R-like proof systems 14. {LK}_{d + 1/2} and combinatorial restrictions 15. F_d and logical restrictions 16. Algebraic and geometric proof systems 17. Feasible interpolation: a framework 18. Feasible interpolation: applications Part IV. Beyond Bounds: 19. Hard tautologies 20. Model theory and lower bounds 21. Optimality 22. The nature of proof complexity Bibliography Special symbols Index.
Introduction Part I. Basic Concepts: 1. Concepts and problems 2. Frege systems 3. Sequent calculus 4. Quantified propositional calculus 5. Resolution 6. Algebraic and geometric proof systems 7. Further proof systems Part II. Upper Bounds: 8. Basic example of the correspondence between theories and proof systems 9. Two worlds of bounded arithmetic 10. Up to EF via the translation 11. Examples of upper bounds and p-simulations 12. Beyond EF via the ... translation Part III. Lower Bounds: 13. R and R-like proof systems 14. {LK}_{d + 1/2} and combinatorial restrictions 15. F_d and logical restrictions 16. Algebraic and geometric proof systems 17. Feasible interpolation: a framework 18. Feasible interpolation: applications Part IV. Beyond Bounds: 19. Hard tautologies 20. Model theory and lower bounds 21. Optimality 22. The nature of proof complexity Bibliography Special symbols Index.
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