Two-Variable Logic with Two Order Relations

@article{Schwentick2012TwoVariableLW,
  title={Two-Variable Logic with Two Order Relations},
  author={Thomas Schwentick and Thomas Zeume},
  journal={Log. Methods Comput. Sci.},
  year={2012},
  volume={8}
}
It is shown that the finite satisfiability problem for two-variable logic over structures with one total preorder relation, its induced successor relation, one linear order relation and some further unary relations is EXPSPACE-complete. Actually, EXPSPACE-completeness already holds for structures that do not include the induced successor relation. As a special case, the EXPSPACE upper bound applies to two-variable logic over structures with two linear orders. A further consequence is that… 

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