A propositional modal logic of time intervals
Journal of the ACM (JACM)
Maintaining knowledge about temporal intervals
Communications of the ACM
An Adequate First Order Interval Logic
COMPOS'97 Revised Lectures from the International Symposium on Compositionality: The Significant Difference
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
SEFM '09 Proceedings of the 2009 Seventh IEEE International Conference on Software Engineering and Formal Methods
An optimal Tableau-based decision algorithm for propositional neighborhood logic
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
Metric Propositional Neighborhood Logics: Expressiveness, Decidability, and Undecidability
Proceedings of the 2010 conference on ECAI 2010: 19th European Conference on Artificial Intelligence
TABLEAUX'11 Proceedings of the 20th international conference on Automated reasoning with analytic tableaux and related methods
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Interval temporal logics provide a natural framework for qualitative and quantitative temporal reasoning over interval structures, where the truth of formulas is defined over intervals rather than points. In this paper, we study the complexity of the satisfiability problem for Metric Propositional Neighborhood Logic (MPNL). MPNL features two modalities to access intervals ''to the left'' and ''to the right'' of the current one, respectively, plus an infinite set of length constraints. MPNL has been recently shown to be decidable over finite linear orders and the natural numbers by a doubly exponential procedure, leaving the tightness of the complexity bound as an open problem. We improve such a result by proving that the satisfiability problem for MPNL over finite linear orders and the natural numbers, as well as over the integers, is actually EXPSPACE-complete, even when length constraints are encoded in binary.