A propositional modal logic of time intervals
Journal of the ACM (JACM)
Maintaining knowledge about temporal intervals
Communications of the ACM
Modal logic
Duration Calculus: A Formal Approach to Real-Time Systems (Monographs in Theoretical Computer Science. an Eatcs Seris)
An Optimal Decision Procedure for Right Propositional Neighborhood Logic
Journal of Automated Reasoning
Optimal Tableaux for Right Propositional Neighborhood Logic over Linear Orders
JELIA '08 Proceedings of the 11th European conference on Logics in Artificial Intelligence
Tableaux for Logics of Subinterval Structures over Dense Orderings
Journal of Logic and Computation
An optimal Tableau-based decision algorithm for propositional neighborhood logic
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
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
Two-sorted Point-Interval Temporal Logics
Electronic Notes in Theoretical Computer Science (ENTCS)
An epistemic Halpern-Shoham logic
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
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We compare the expressiveness of the fragments of Halpern and Shoham's interval logic (HS), i.e., of all interval logics with modal operators associated with Allen's relations between intervals in linear orders. We establish a complete set of inter-definability equations between these modal operators, and thus obtain a complete classification of the family of 212 fragments of HS with respect to their expressiveness. Using that result and a computer program, we have found that there are 1347 expressively different such interval logics over the class of all linear orders.