Handbook of theoretical computer science (vol. B)
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
Modal logic
On the temporal analysis of fairness
POPL '80 Proceedings of the 7th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Temporal Logic with Forgettable Past
LICS '02 Proceedings of the 17th Annual IEEE Symposium on Logic in Computer Science
Sharpening the Undecidability of Interval Temporal Logic
ASIAN '00 Proceedings of the 6th Asian Computing Science Conference on Advances in Computing Science
Proceedings of the Conference on Logic of Programs
The Declarative Past and Imperative Future: Executable Temporal Logic for Interactive Systems
Temporal Logic in Specification
An Optimal Decision Procedure for Right Propositional Neighborhood Logic
Journal of Automated Reasoning
Tight bounds on the complexity of cascaded decomposition of automata
SFCS '90 Proceedings of the 31st Annual Symposium on Foundations of Computer Science
LPAR '08 Proceedings of the 15th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning
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
A decidable spatial logic with cone-shaped cardinal directions
CSL'09/EACSL'09 Proceedings of the 23rd CSL international conference and 18th EACSL Annual conference on Computer science logic
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
TABLEAUX'11 Proceedings of the 20th international conference on Automated reasoning with analytic tableaux and related methods
The Ultimate Undecidability Result for the Halpern-Shoham Logic
LICS '11 Proceedings of the 2011 IEEE 26th Annual Symposium on Logic in Computer Science
What's Decidable about Halpern and Shoham's Interval Logic? The Maximal Fragment ABBL
LICS '11 Proceedings of the 2011 IEEE 26th Annual Symposium on Logic in Computer Science
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In our contribution, we study the effects of adding past operators to interval temporal logics. We focus our attention on the representative case of Propositional Neighborhood Logic ( $\mathsf{A \overline A}$ for short), taking into consideration different temporal domains. $\mathsf{A \overline A}$ is the proper fragment of Halpern and Shoham's modal logic of intervals with modalities for Allen's relations meets (future modality) and met by (past modality). We first prove that, unlike what happens with point-based linear temporal logic, $\mathsf{A \overline A}$ is strictly more expressive than its future fragment A. Then, we show that there is a log-space reduction from the satisfiability problem for $\mathsf{A \overline A}$ over ℤ to its satisfiability problem over ℕ. Compared to the corresponding reduction for point-based linear temporal logic, the one for $\mathsf{A \overline A}$ turns out to be much more involved. Finally, we prove that $\mathsf{A \overline A}$ is able to separate ℚ and ℝ, while A is not.