Abstract
We study the complexity of the model checking problem, for fixed models A, 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 A, 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.
This research was supported by EPSRC grant EP/C54384X/1.
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Martin, B. (2008). First-Order Model Checking Problems Parameterized by the Model . In: Beckmann, A., Dimitracopoulos, C., Löwe, B. (eds) Logic and Theory of Algorithms. CiE 2008. Lecture Notes in Computer Science, vol 5028. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69407-6_45
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DOI: https://doi.org/10.1007/978-3-540-69407-6_45
Publisher Name: Springer, Berlin, Heidelberg
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