Undecidability of the Logic of Overlap Relation over Discrete Linear Orderings
Electronic Notes in Theoretical Computer Science (ENTCS)
B and D are enough to make the Halpern-Shoham logic undecidable
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming: Part II
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume Two
The importance of the past in interval temporal logics: the case of propositional neighborhood logic
Logic Programs, Norms and Action
A survey on temporal logics for specifying and verifying real-time systems
Frontiers of Computer Science: Selected Publications from Chinese Universities
Adding an Equivalence Relation to the Interval Logic ABB: Complexity and Expressiveness
LICS '13 Proceedings of the 2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science
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In this article, we develop tableau-based decision procedures for the logics of subinterval structures over dense linear orderings. In particular, we consider the two difficult cases: the relation of strict subintervals (with both endpoints strictly inside the current interval) and the relation of proper subintervals (that can share one endpoint with the current interval). For each of these logics, we establish a small pseudo-model property and construct a sound, complete and terminating tableau that searches systematically for existence of such a pseudo-model satisfying the input formulas. Both constructions are non-trivial, but the latter is substantially more complicated because of the presence of beginning and ending subintervals which require special treatment. We prove PSPACE completeness for both procedures and implement them in the generic tableau-based theorem prover Lotrec.