A propositional modal logic of time intervals
Journal of the ACM (JACM)
Maintaining knowledge about temporal intervals
Communications of the ACM
Modal logic
A Hardware Semantics Based on Temporal Intervals
Proceedings of the 10th Colloquium on Automata, Languages and Programming
An Adequate First Order Interval Logic
COMPOS'97 Revised Lectures from the International Symposium on Compositionality: The Significant Difference
A Tableau Method for Interval Temporal Logic with Projection
TABLEAUX '98 Proceedings of the International Conference on Automated Reasoning with Analytic Tableaux and Related Methods
Reasoning about digital circuits
Reasoning about digital circuits
Temporalized logics and automata for time granularity
Theory and Practice of Logic Programming
Journal of Logic, Language and Information
LPAR '08 Proceedings of the 15th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning
Complete and Terminating Tableau for the Logic of Proper Subinterval Structures Over Dense Orderings
Electronic Notes in Theoretical Computer Science (ENTCS)
An optimal Tableau-based decision algorithm for propositional neighborhood logic
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
A tableau-based decision procedure for right propositional neighborhood logic
TABLEAUX'05 Proceedings of the 14th international conference on Automated Reasoning with Analytic Tableaux and Related Methods
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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Logics for time intervals provide a natural framework for representing and reasoning about timing properties in various areas of artificial intelligence and computer science. Unfortunately, most interval temporal logics proposed in the literature have been shown to be (highly) undecidable. Decidable fragments of these logics have been obtained by imposing severe restrictions on their expressive power.In this paper, we propose a new interval temporal logic, called Split Logic, which is equipped with operators borrowed from other interval temporal logics, but is interpreted over specific interval structures based on a layered view of the temporal domain. We show that there exists a straightforward correspondence between Split Logic and the first-order fragments of the monadic theories of time granularity proposed in the literature. This connection allows us to transfer existing decidability results for such theories to Split Logic.