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Bounded variable logics and counting : a study in finite models /
Since their inception, the 'Perspectives in Logic' and 'Lecture Notes in Logic' series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. In this volume, the ninth publ...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge ; New York :
Cambridge University Press,
2017.
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| Colección: | Lecture notes in logic ;
9. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Cover; Half-title; Series information; Title page; Copyright information; Preface; Table of contents; 0. Introduction; 0.1 Finite Models, Logic and Complexity; 0.1.1 Logics for Complexity Classes; 0.1.2 Semantically Defined Classes; 0.1.3 Which Logics Are Natural?; 0.2 Natural Levels of Expressiveness; 0.2.1 Fixed-Point Logics and Their Counting Extensions; 0.2.2 The Framework of Infinitary Logic; 0.2.3 The Role of Order and Canonization ; 0.3 Guide to the Exposition; 1. Definitions and Preliminaries; 1.1 Structures and Types; 1.1.1 Structures; 1.1.2 Queries and Global Relations; 1.1.3 Logics
- 1.1.4 Types1.2 Algorithms on Structures; 1.2.1 Complexity Classes and Presentations; 1.2.2 Logics for Complexity Classes; 1.3 Some Particular Logics; 1.3.1 First-Order Logic and Infinitary Logic; 1.3.2 Fragments of Infinitary Logic; 1.3.3 Fixed-Point Logics; 1.3.4 Fixed-Point Logics and the L[sup(k)sub([infty][textomega])] ; 1.4 Types and Definability in the L[sup(k)sub([infty][textomega])] and C[sup(k)sub([infty][textomega])] ; 1.5 Interpretations; 1.5.1 Variants of Interpretations; 1.5.2 Examples; 1.5.3 Interpretations and Definability; 1.6 Lindstrom Quantifiers and Extensions ; 1.6.1 Cardinality Lindstrom Quantifiers
- 1.6.2 Aside on Uniform Families of Quantifiers1.7 Miscellaneous; 1.7.1 Canonization and Invariants; 1.7.2 Orderings and Pre-Orderings; 1.7.3 Lexicographic Orderings; 2. The Games and Their Analysis; 2.1 The Pebble Games for L[sup(k)sub([infty][textomega])] and C[sup(k)sub([infty][textomega])] ; 2.1.1 Examples and Applications; 2.1.2 Proof of Theorem 2.2; 2.1.3 Further Analysis of the C[sup(k)]-Game; 2.1.4 The Analogous Treatment for L[sup(k)]; 2.2 Colour Refinement and the Stable Colouring; 2.2.1 The Standard Case: Colourings of Finite Graphs; 2.2.2 Definability of the Stable Colouring
- 2.2.3 C[sup(2)sub([infty][textomega])] and the Stable Colouring 2.2.4 A Variant Without Counting; 2.3 Order in the Analysis of the Games; 2.3.1 The Internal View; 2.3.2 The External View; 2.3.3 The Analogous Treatment for L[sup(k)]; 3. The Invariants; 3.1 Complete Invariants for L[sup(k)] and C[sup(k)]; 3.2 The C[sup(k)]-Invariants; 3.3 The L[sup(k)]-Invariants; 3.4 Some Applications; 3.4.1 Fixed-Points and the Invariants; 3.4.2 The Abiteboul-Vianu Theorem; 3.4.3 Comparison of I[sub(C[sup(k)])] and I[sub(L[sup(k)])]; 3.5 A Partial Reduction to Two Variables; 4. Fixed-Point Logic with Counting
- 4.1 Definition of FP+C and PFP+C4.2 FP+C and the C[sup(k)]-Invariants; 4.3 The Separation from PTIME; 4.4 Other Characterizations of FP+C; 5. Related Lindstr[ddot(o)]m Extensions; 5.1 A Structural Padding Technique; 5.2 Cardinality Lindstrom Quantifiers ; 5.2.1 Proof of Theorem 5.1; 5.3 Aside on Further Applications; 6. Canonization Problems; 6.1 Canonization; 6.2 PTIME Canonization and Fragments of PTIME; 6.3 Canonization and Inversion of the Invariants; 6.4 A Reduction to Three Variables; 6.4.1 The Proof of Theorems 6.16 and 6.17; 6.4.2 Remarks on Further Reduction