Finite Model Theory and Its Applications

  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},
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. 

Finite Model Theory on Tame Classes of Structures

  • A. Dawar
  • Mathematics, Computer Science
  • 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

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

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

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

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

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

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

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

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.



Finite model theory

The text presents the main results of descriptive complexity theory, the connection between axiomatizability of classes of finite structures and their complexity with respect to time and space bounds.

Elements of Finite Model Theory

  • L. Libkin
  • Computer Science
    Texts in Theoretical Computer Science
  • 2004
This book describes applications in databases, complexity theory, and formal languages, as well as other branches of computer science, and highlights the computer science aspects of the subject.

Finite model theory and finite variable logics

In this dissertation, I investigate some questions about the model theory of finite structures. One goal is to better understand the expressive power of various logical languages, including

Toward logic tailored for computational complexity

This work discusses the first- order theory of finite structures and alternatives to first-order logic, especially polynomial time logic.

A Characterisation of First-Order Constraint Satisfaction Problems

It is decidable to determine whether a constraint satisfaction problem is first-order definable, and the general problem is shown to be NP-complete, and a polynomial-time algorithm is given in the case of cores.

Pseudo-finite homogeneity and saturation

It is shown that a stable theory has the pseudo-finite homogeneity property just in case its expressive power for finite states is bounded and the corresponding pseudo- finite saturation property is introduced.

Stability theory, permutations of indiscernibles, and embedded finite models

We show that the expressive power of first-order logic over finite models embedded in a model M is determined by stability-theoretic properties of M . In particular, we show that if M is stable, then

Existential positive types and preservation under homomorphisms

  • Benjamin Rossman
  • Mathematics
    20th Annual IEEE Symposium on Logic in Computer Science (LICS' 05)
  • 2005
We prove the finite homomorphism preservation theorem: a first-order formula is preserved under homomorphisms on finite structures iff it is equivalent in the finite to an existential positive