Journal of the ACM (JACM)
On the complexity of integer programming
Journal of the ACM (JACM)
Modal logic
The Complexity of the Graded µ-Calculus
CADE-18 Proceedings of the 18th International Conference on Automated Deduction
Reasoning with Individuals for the Description Logic SHIQ
CADE-17 Proceedings of the 17th International Conference on Automated Deduction
Theoretical Computer Science
The description logic handbook
On the undecidability of logics with converse, nominals, recursion and counting
Artificial Intelligence
XML schema, tree logic and sheaves automata
Applicable Algebra in Engineering, Communication and Computing
A set-theoretic approach to automated deduction in graded modal logics
IJCAI'97 Proceedings of the 15th international joint conference on Artifical intelligence - Volume 1
XML schema, tree logic and sheaves automata
RTA'03 Proceedings of the 14th international conference on Rewriting techniques and applications
On the complexity of equational horn clauses
CADE' 20 Proceedings of the 20th international conference on Automated Deduction
Automata and logics for unranked and unordered trees
RTA'05 Proceedings of the 16th international conference on Term Rewriting and Applications
Shallow Models for Non-iterative Modal Logics
KI '08 Proceedings of the 31st annual German conference on Advances in Artificial Intelligence
PSPACE bounds for rank-1 modal logics
ACM Transactions on Computational Logic (TOCL)
CoLoSS: The Coalgebraic Logic Satisfiability Solver
Electronic Notes in Theoretical Computer Science (ENTCS)
FOSSACS '09 Proceedings of the 12th International Conference on Foundations of Software Science and Computational Structures: Held as Part of the Joint European Conferences on Theory and Practice of Software, ETAPS 2009
An easy completeness proof for the modal µ-calculus on finite trees
FOSSACS'10 Proceedings of the 13th international conference on Foundations of Software Science and Computational Structures
VoCS'08 Proceedings of the 2008 international conference on Visions of Computer Science: BCS International Academic Conference
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part II
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We introduce a Presburger modal logic PML with regularity constraints and full Presburger constraints on the number of children that generalize graded modalities, also known as number restrictions in description logics. We show that PML satisfiability is only pspace-complete by designing a Ladner-like algorithm that can be turned into an analytic proof system. algorithm. This extends a well-known and non-trivial pspace upper bound for graded modal logic. Furthermore, we provide a detailed comparison with logics that contain Presburger constraints and that are dedicated to query XML documents. As an application, we show that satisfiability for Sheaves Logic SL is pspace-complete, improving significantly its best known upper bound.