Handbook of theoretical computer science (vol. B)
A propositional modal logic of time intervals
Journal of the ACM (JACM)
Maintaining knowledge about temporal intervals
Communications of the ACM
Sharpening the Undecidability of Interval Temporal Logic
ASIAN '00 Proceedings of the 6th Asian Computing Science Conference on Advances in Computing Science
Decidability of Interval Temporal Logics over Split-Frames via Granularity
JELIA '02 Proceedings of the European Conference on Logics in Artificial Intelligence
Reasoning about temporal relations: The tractable subalgebras of Allen's interval algebra
Journal of the ACM (JACM)
An Optimal Decision Procedure for Right Propositional Neighborhood Logic
Journal of Automated Reasoning
On Decidability and Expressiveness of Propositional Interval Neighborhood Logics
LFCS '07 Proceedings of the international symposium on Logical Foundations of Computer Science
Tableau Systems for Logics of Subinterval Structures over Dense Orderings
TABLEAUX '07 Proceedings of the 16th international conference on Automated Reasoning with Analytic Tableaux and Related Methods
Non-finite Axiomatizability and Undecidability of Interval Temporal Logics with C, D, and T
CSL '08 Proceedings of the 22nd international workshop on Computer Science Logic
Optimal Tableaux for Right Propositional Neighborhood Logic over Linear Orders
JELIA '08 Proceedings of the 11th European conference on Logics in Artificial Intelligence
An optimal Tableau-based decision algorithm for propositional neighborhood logic
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
Back to Interval Temporal Logics
ICLP '08 Proceedings of the 24th International Conference on Logic Programming
Undecidability of the Logic of Overlap Relation over Discrete Linear Orderings
Electronic Notes in Theoretical Computer Science (ENTCS)
Metric Propositional Neighborhood Logics: Expressiveness, Decidability, and Undecidability
Proceedings of the 2010 conference on ECAI 2010: 19th European Conference on Artificial Intelligence
Maximal decidable fragments of Halpern and Shoham's modal logic of intervals
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming: Part II
B and D are enough to make the Halpern-Shoham logic undecidable
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming: Part II
Hybrid Metric Propositional Neighborhood Logics with Interval Length Binders
Electronic Notes in Theoretical Computer Science (ENTCS)
Two-sorted Point-Interval Temporal Logics
Electronic Notes in Theoretical Computer Science (ENTCS)
The importance of the past in interval temporal logics: the case of propositional neighborhood logic
Logic Programs, Norms and Action
Proceedings of the twelfth workshop on Foundations of genetic algorithms XII
A survey on temporal logics for specifying and verifying real-time systems
Frontiers of Computer Science: Selected Publications from Chinese Universities
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Interval temporal logics are based on temporal structures where time intervals, rather than time instants, are the primitive ontological entities. They employ modal operators corresponding to various relations between intervals, known as Allen's relations. Technically, validity in interval temporal logics translates to dyadic second-order logic, thus explaining their complex computational behavior. The full modal logic of Allen's relations, called HS, has been proved to be undecidable by Halpern and Shoham under very weak assumptions on the class of interval structures, and this result was discouraging attempts for practical applications and further research in the field. A renewed interest has been recently stimulated by the discovery of interesting decidable fragments of HS. This paper contributes to the characterization of the boundary between decidability and undecidability of HS fragments. It summarizes known positive and negative results, it describes the main techniques applied so far in both directions, and it establishes a number of new undecidability results for relatively small fragments of HS.