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The Classical Decision Problem
TLDR
The Undecidable Standard Classes for Pure Predicate Logic, a Treatise on the Transformation of the Classical Decision Problem, and some Results and Open Problems are presented.
On The Restraining Power of Guards
  • E. Grädel
  • Mathematics, Computer Science
    J. Symb. Log.
  • 1 December 1999
TLDR
It is proved that the satisfiability problems for the guarded fragment and the loosely guarded fragment of first-order logic are complete for deterministic double exponential time, and a tree model property is established for both the guarded fragments and the closely guarded fragment.
On the decision problem for two-variable first-order logic
TLDR
Improve Mortimer's bound by one exponential and show that every satisfiable FO2-sentence has a model whose size is at most exponential in the size of the sentence, establishing that the satisfiability problem for FO2 is NEXPTIME-complete.
Automatic structures
TLDR
This work determines the complexity of model checking and query evaluation on automatic structures for fragments of first-order logic and gives model-theoretic characterisations for automatic structures via interpretations.
Automata logics, and infinite games: a guide to current research
A central aim and ever-lasting dream of computer science is to put the development of hardware and software systems on a mathematical basis which is both firm and practical. Such a scientific
Dependence and Independence
TLDR
Y gives rise to a natural logic capable of formalizing basic intuitions about independence and dependence and can be used to give partially ordered quantifiers and IF-logic an alternative interpretation without some of the shortcomings related to so called signaling that interpretations using =$$(vec{x, \vec{y})}$$ have.
Finite Model Theory and Its Applications
TLDR
Themes in Finite Model Theory and Descriptive Complexity, Logic and Random Structures, Embedded Finite Models and Constraint Databases, and Local Variations on a Loose Theme.
Guarded fixed point logic
TLDR
It is proved that the satisfiability problems for guarded fixed point logics are decidable and complete for deterministic double exponential time.
Finite Presentations of Infinite Structures: Automata and Interpretations
TLDR
The model checking problem for FO(∃ω), first-order logic extended by the quantifier “there are infinitely many”, is proved to be decidable for automatic and ω-automatic structures and appropriate expansions of the real ordered group.
Automata Logics, and Infinite Games
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