On model-theoretic approaches to monadic second-order logic evaluation

Abstract

We review the model-theoretic approaches to Monadic Second-Order Logic (MSO) evaluation, especially to model-checking on MSOL-inductive classes of structures. Starting our study with finite strings and finite trees, we then focus on classes of structures of bounded treewidth. For these classes we define the ``model-theoretical automaton'' which generalizes the corresponding automaton defined by Ladner for strings. First we prove that the model-theoretical automaton cannot be used as an MSO model-checking algorithm on any of these classes of structures. Then we study its relationship with other classical model-theoretic methods as well as its relationship with recent datalog-based approaches to the MSO model-checking problem.