Finite Model Theory and Its ApplicationsErich Grädel, Phokion G. Kolaitis, Leonid Libkin, Maarten Marx, Joel Spencer, Moshe Y. Vardi, Yde Venema, Scott Weinstein Springer Science & Business Media, 24.04.2007 - 437 Seiten Finite model theory,as understoodhere, is an areaof mathematicallogic that has developed in close connection with applications to computer science, in particular the theory of computational complexity and database theory. One of the fundamental insights of mathematical logic is that our understanding of mathematical phenomena is enriched by elevating the languages we use to describe mathematical structures to objects of explicit study. If mathematics is the science of patterns, then the media through which we discern patterns, as well as the structures in which we discern them, command our attention. It isthis aspect oflogicwhichis mostprominentin model theory,“thebranchof mathematical logic which deals with the relation between a formal language and its interpretations”. No wonder, then, that mathematical logic, and ?nite model theory in particular, should ?nd manifold applications in computer science: from specifying programs to querying databases, computer science is rife with phenomena whose understanding requires close attention to the interaction between language and structure. This volume gives a broadoverviewof some central themes of ?nite model theory: expressive power, descriptive complexity, and zero–one laws, together with selected applications to database theory and arti?cial intelligence, es- cially constraint databases and constraint satisfaction problems. The ?nal chapter provides a concise modern introduction to modal logic,which emp- sizes the continuity in spirit and technique with ?nite model theory. |
Inhalt
Contents | 1 |
On the Expressive Power of Logics on Finite Models 27 | 26 |
References | 116 |
Finite Model Theory and Descriptive Complexity | 125 |
Logic and Random Structures | 222 |
པ | 257 |
A Logical Approach to Constraint Satisfaction 339 | 338 |
| 367 | |
| 431 | |
Andere Ausgaben - Alle anzeigen
Finite Model Theory and Its Applications Erich Grädel,Phokion G. Kolaitis,Leonid Libkin,Maarten Marx,Joel Spencer,Moshe Y. Vardi,Yde Venema,Scott Weinstein Eingeschränkte Leseprobe - 2007 |
Finite Model Theory and Its Applications Erich Grädel,Phokion G. Kolaitis,Leonid Libkin,Maarten Marx,Joel Spencer,Moshe Y. Vardi,Yde Venema,Scott Weinstein Keine Leseprobe verfügbar - 2014 |
Finite Model Theory and Its Applications Erich Grädel,Phokion G. Kolaitis,Leonid Libkin,Maarten Marx,Joel Spencer,Moshe Y. Vardi,Yde Venema,Scott Weinstein Keine Leseprobe verfügbar - 2009 |
Häufige Begriffe und Wortgruppen
adom algorithm arity basic modal binary relation bisimulation Boolean query bounded captures PTIME class of finite complexity classes Computer Science constraint databases constraint satisfaction CSP(B data complexity Datalog Datalog program Definition denote domain Duplicator wins Ehrenfeucht-Fraïssé game elements encoding equivalent example existential expressive power Fagin's Theorem finite graphs finite model theory finite structures first-order definable first-order formula first-order logic first-order sentence fixed-point logic FO(SC FOact SC fragment function given graph G greatest fixed points homomorphism induction infinitary logic infinite input isomorphism k-pebble game L-definable language least fixed point Lemma linear order metafinite modal logic modal system model-checking monadic monotone mosaic nodes NP-complete o-minimal o-structures operator Player polynomial polynomial-time positive integer predicate proof Proposition PSPACE PTIME query Q recursive relation symbol result satisfiability problem second-order logic Spoiler subformula Theorem tuple unary Vardi variables vocabulary winning strategy