Artificial Intelligence Review
Guarded fixed point logics and the monadic theory of countable trees
Theoretical Computer Science - Complexity and logic
Computational Space Efficiency and Minimal Model Generation for Guarded Formulae
LPAR '01 Proceedings of the Artificial Intelligence on Logic for Programming
Games and Model Checking for Guarded Logics
LPAR '01 Proceedings of the Artificial Intelligence on Logic for Programming
EXPSPACE-Complete Variant of Guarded Fragment with Transitivity
STACS '02 Proceedings of the 19th Annual Symposium on Theoretical Aspects of Computer Science
CADE-16 Proceedings of the 16th International Conference on Automated Deduction: Automated Deduction
Invited Talk: Rewrite-based Deduction and Symbolic Constraints
CADE-16 Proceedings of the 16th International Conference on Automated Deduction: Automated Deduction
Deciding the guarded fragments by resolution
Journal of Symbolic Computation
Encoding two-valued nonclassical logics in classical logic
Handbook of automated reasoning
Paramodulation with Built-In Abelian Groups
LICS '00 Proceedings of the 15th Annual IEEE Symposium on Logic in Computer Science
Hyperresolution for guarded formulae
Journal of Symbolic Computation - Special issue: First order theorem proving
Automata logics, and infinite games
Journal of Symbolic Computation
Superposition with completely built-in Abelian groups
Journal of Symbolic Computation
Deciding Regular Grammar Logics with Converse Through First-Order Logic
Journal of Logic, Language and Information
On the complexity of the two-variable guarded fragment with transitive guards
Information and Computation
The axiomatic translation principle for modal logic
ACM Transactions on Computational Logic (TOCL)
CTL Model-Checking with Graded Quantifiers
ATVA '08 Proceedings of the 6th International Symposium on Automated Technology for Verification and Analysis
Decidability of the Guarded Fragment with the Transitive Closure
ICALP '09 Proceedings of the 36th Internatilonal Collogquium on Automata, Languages and Programming: Part II
Graded-CTL: Satisfiability and Symbolic Model Checking
ICFEM '09 Proceedings of the 11th International Conference on Formal Engineering Methods: Formal Methods and Software Engineering
Fundamenta Informaticae - Advances in Computational Logic (CIL C08)
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
Modal Access Control LogicAxiomatization, Semantics and FOL Theorem Proving
Proceedings of the 2010 conference on STAIRS 2010: Proceedings of the Fifth Starting AI Researchers' Symposium
On the finite satisfiability problem for the guarded fragment with transitivity
LPAR'05 Proceedings of the 12th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
Counting in the two variable guarded logic with transitivity
STACS'05 Proceedings of the 22nd annual conference on Theoretical Aspects of Computer Science
Results on the guarded fragment with equivalence or transitive relations
CSL'05 Proceedings of the 19th international conference on Computer Science Logic
Fundamenta Informaticae - Advances in Computational Logic (CIL C08)
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 consider the restriction of the guarded fragment to the two-variable case where, in addition, binary relations may be specified as transitive. We show that (i) this very restricted form of the guarded fragment without equality is undecidable and that (ii) when allowing non-unary relations to occur only in guards, the logic becomes decidable. The latter subclass of the guarded fragment is the one that occurs naturally when translating multi-modal logics of the type K4, S4 or S5 into first-order logic. We also show that the loosely guarded fragment without equality and with a single transitive relation is undecidable.