Theoretical Computer Science
EXPSPACE-Complete Variant of Guarded Fragment with Transitivity
STACS '02 Proceedings of the 19th Annual Symposium on Theoretical Aspects of 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
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
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
Counting in the two variable guarded logic with transitivity
STACS'05 Proceedings of the 22nd annual conference on Theoretical Aspects of Computer Science
On the complexity of the two-variable guarded fragment with transitive guards
Information and Computation
On finite satisfiability of the guarded fragment with equivalence or transitive guards
LPAR'07 Proceedings of the 14th international conference on Logic for programming, artificial intelligence and reasoning
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
Complexity of two-variable logic on finite trees
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part II
Querying the guarded fragment with transitivity
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part II
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We study the problem of the satisfiability of guarded formulas in models in which some distinguished binary symbols are interpreted as equivalence relations or as transitive relations. We sharpen the undecidability result for the two-variable guarded fragment with transitive relations by reducing the number of transitive relations to two. We prove that the satisfiability problem for the two-variable guarded fragment with two equivalence relations is 2EXPTIME-complete. We consider the guarded fragment with equivalence relations in guards and show that this variant is easily reducible to the variant with transitive relations in guards. However, in the case of two variables, the version with equivalence relations is easier: NEXPTIME-complete. Finally we show that the decidability results for the guarded fragment with either equivalence relations or transitive relations in guards cannot be generalized to the loosely guarded fragment.