# Finite Model Theory and Its Applications

@inproceedings{Grdel2007FiniteMT, title={Finite Model Theory and Its Applications}, author={Erich Gr{\"a}del and Phokion G. Kolaitis and Leonid Libkin and maarten marx and Joel H. Spencer and Moshe Y. Vardi and Yde Venema and Scott Weinstein}, booktitle={Texts in Theoretical Computer Science. An EATCS Series}, year={2007} }

Unifying Themes in Finite Model Theory.- On the Expressive Power of Logics on Finite Models.- Finite Model Theory and Descriptive Complexity.- Logic and Random Structures.- Embedded Finite Models and Constraint Databases.- A Logical Approach to Constraint Satisfaction.- Local Variations on a Loose Theme: Modal Logic and Decidability.

## 200 Citations

### Finite Model Theory on Tame Classes of Structures

- Mathematics, Computer ScienceMFCS
- 2007

Some results in finite model theory are reviewed and the connection between logic and algorithms is explored and some classes that are known to be algorithmically well-behaved are reviewed.

### Finite domain and symbolic inference methods for extensions of first-order logic

- PhilosophyAI Commun.
- 2011

This dissertation studies the tasks of constraint propagation, grounding, model revision, and debugging for FO(·), a rich extension of classical logic with, amongst others, inductive definitions and aggregates.

### The mu-calculus and Model Checking

- Computer ScienceHandbook of Model Checking
- 2018

This chapter presents that part of the theory of the \(\mu\)-calculus that is relevant to the model-checking problem as broadly understood. The \(\mu\)-calculus is one of the most important logics in…

### Automata-based presentations of infinite structures

- Computer ScienceFinite and Algorithmic Model Theory
- 2011

Algorithmic model theory aims to extend in a systematic fashion the approach and methods of finite model theory, and its interactions with computer science, from finite structures to finitely-presentable infinite ones.

### The finite model theory toolbox of a database theoretician

- Computer SciencePODS
- 2009

Finite model theory has built a large arsenal of tools that can easily be used by database theoreticians without going to the basics such as combinatorial games, and such tools are surveyed here.

### Definability and model checking: the role of orders and compositionality

- Computer Science
- 2011

This thesis studies how the expressive power of logics over finite structures is affected by the presence of orders, and investigates structures with weaker forms of orderings, namely locally ordered graphs, in which only the neighbourhoods of the vertices are linearly ordered.

### Introduction and Technical Preliminaries

- Computer Science
- 2014

Chapter 1 is a formal and short introduction to different topics and concepts: logics, (co)algebras, databases, schema mappings and category theory, in order to render this monograph more…

### Coherence and Computational Complexity of Quantifier-free Dependence Logic Formulas

- Computer Science, MathematicsStud Logica
- 2013

Three thresholds in the complexity of the model checking problem for quantifier-free dependence logic are characterized: logarithmic space, non-deterministic logarithsmic space and non-Deterministic polynomial time.

### Model-Checking the Higher-Dimensional Modal mu-Calculus

- Computer ScienceFICS
- 2012

This paper investigates how the model checking problem of the higher-dimensional modal -calculus can be eciently implemented and proposes two generic algorithms, based on extensions of local model checking and symbolic model checking algorithms respectively.

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