First-order model checking problems parameterized by the model

Martin, Barnaby (2008) First-order model checking problems parameterized by the model. Logic and Theory of Algorithms. In: The 4th Conference on Computability in Europe: Logic and Theory of Algorithms (CiE 2008), 15-20 June, 2008, University of Athens, Greece. ISBN 9783540694052. ISSN 0302-9743 [Conference or Workshop Item] (doi:10.1007/978-3-540-69407-6_45)

Abstract

We study the complexity of the model checking problem, for fixed models <em>A</em>, over certain fragments $\mathcal{L}$ of first-order logic, obtained by restricting which of the quantifiers and boolean connectives we permit. These are sometimes known as the expression complexities of $\mathcal{L}$. We obtain various full and partial complexity classification theorems for these logics $\mathcal{L}$ as each ranges over models <em>A</em>, in the spirit of the dichotomy conjecture for the Constraint Satisfaction Problem --- which itself may be seen as the model checking problem for existential conjunctive positive first-order logic.

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