Theoretical Computer Science
Small Substructures and Decidability Issues for First-Order Logic with Two Variables
LICS '05 Proceedings of the 20th Annual IEEE Symposium on Logic in Computer Science
Two-Variable Logic on Words with Data
LICS '06 Proceedings of the 21st Annual IEEE Symposium on Logic in Computer Science
Qualitative Spatial Representation and Reasoning: An Overview
Fundamenta Informaticae - Qualitative Spatial Reasoning
LTL with the freeze quantifier and register automata
ACM Transactions on Computational Logic (TOCL)
On Finite Satisfiability of Two-Variable First-Order Logic with Equivalence Relations
LICS '09 Proceedings of the 2009 24th Annual IEEE Symposium on Logic In Computer Science
Future-Looking Logics on Data Words and Trees
MFCS '09 Proceedings of the 34th International Symposium on Mathematical Foundations of Computer Science 2009
Automata and logics for words and trees over an infinite alphabet
CSL'06 Proceedings of the 20th international conference on Computer Science Logic
Two variables and two successors
MFCS'10 Proceedings of the 35th international conference on Mathematical foundations of computer science
Two-Variable First-Order Logic with Equivalence Closure
LICS '12 Proceedings of the 2012 27th Annual IEEE/ACM Symposium on Logic in Computer Science
An Automata Model for Trees with Ordered Data Values
LICS '12 Proceedings of the 2012 27th Annual IEEE/ACM Symposium on Logic in Computer Science
Extending two-variable logic on data trees with order on data values and its automata
ACM Transactions on Computational Logic (TOCL)
Two-Variable Logic with Counting and Trees
LICS '13 Proceedings of the 2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science
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The finite satisfiability problem for two-variable logic over structures with unary relations and two order relations is investigated. Firstly, decidability is shown for structures with one total preorder relation and one linear order relation. More specifically, we show that this problem is complete for EXPSPACE. As a consequence, the same upper bound applies to the case of two linear orders. Secondly, we prove undecidability for structures with two total preorder relations as well as for structures with one total preorder and two linear order relations. Further, we point out connections to other logics. Decidability is shown for two-variable logic on data words with orders on both positions and data values, but without a successor relation. We also study "partial models" of compass and interval temporal logic and prove decidability for some of their fragments.