Propositional interval temporal logics come into play in many areas of artificial intelligence and computer science. Unfortunately, most of them turned out to be (highly) undecidable. Some positive exceptions, belonging to the classes of neighborhood logics and of logics of subinterval relations, have been recently identified. In this paper, we address the decision problem for the future fragment of Propositional Neighborhood Logic (Right Propositional Neighborhood Logic) interpreted over trees and we positively solve it by providing a tableau-based decision procedure that works in exponential space. Moreover, we prove that the decision problem for the logic is EXPSPACE-hard, thus showing the optimality of the proposed procedure.
