Structural complexity 2
Complexity Results for First-Order Two-Variable Logic with Counting
SIAM Journal on Computing
Invited Talk: Decision procedures for guarded logics
CADE-16 Proceedings of the 16th International Conference on Automated Deduction: Automated Deduction
Complexity of Two-Variable Logic with Counting
LICS '97 Proceedings of the 12th Annual IEEE Symposium on Logic in Computer Science
Two-variable logic with counting is decidable
LICS '97 Proceedings of the 12th Annual IEEE Symposium on Logic in Computer Science
LICS '99 Proceedings of the 14th Annual IEEE Symposium on Logic in Computer Science
The Two-Variable Guarded Fragment with Transitive Relations
LICS '99 Proceedings of the 14th Annual IEEE Symposium on Logic in Computer Science
On the Decision Problem for the Guarded Fragment with Transitivity
LICS '01 Proceedings of the 16th Annual IEEE Symposium on Logic in Computer Science
The two-variable guarded fragment with transitive guards is 2EXPTIME-hard
FOSSACS'03/ETAPS'03 Proceedings of the 6th International conference on Foundations of Software Science and Computation Structures and joint European conference on Theory and practice of software
How to decide query containment under constraints using a description logic
LPAR'00 Proceedings of the 7th international conference on Logic for programming and automated reasoning
Data-complexity of the two-variable fragment with counting quantifiers
Information and Computation
Results on the guarded fragment with equivalence or transitive relations
CSL'05 Proceedings of the 19th international conference on Computer Science Logic
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We show that the extension of the two-variable guarded fragment with transitive guards (GF+TG) by functionality statements is undecidable. This gives immediately undecidability of the extension of GF+TG by counting quantifiers. The result is optimal, since both the three-variable fragment of the guarded fragment with counting quantifiers and the two-variable guarded fragment with transitivity are undecidable. We also show that the extension of GF+TG with functionality, where functional predicate letters appear in guards only, is decidable and of the same complexity as GF+TG. This fragment captures many expressive modal and description logics.