Decidability of the Logics of the Reflexive Sub-interval and Super-interval Relations over Finite Linear Orders

Angelo Montanari, Ian Pratt-Hartmann, Pietro Sala
2010 2010 17th International Symposium on Temporal Representation and Reasoning  
An interval temporal logic is a propositional, multimodal logic interpreted over interval structures of partial orders. The semantics of each modal operator are given in the standard way with respect to one of the natural accessibility relations defined on such interval structures. In this paper, we consider the modal operators based on the (reflexive) subinterval relation and the (reflexive) super-interval relation. We show that the satisfiability problems for the interval temporal logics
more » ... emporal logics featuring either or both of these modalities, interpreted over interval structures of finite linear orders, are all PSPACEcomplete. These results fill a gap in the known complexity results for interval temporal logics.
doi:10.1109/time.2010.18 dblp:conf/time/MontanariPS10 fatcat:o76ols4ff5dm3ouuh74ytavepe