R. Li and J. Carmo, "On completeness of a positional interval logic with equality, overlap and subinterval relations", Journal of the IGPL (Interest Group on Propositional and Predicate Logic), 1995, Vol. 3, No. 5, pp. 765--790.
A new logic for reasoning about time intervals is presented and proven to be complete in the standard logical sense: if a statement $S$ is true in all possible situations, then $S$ can be deduced from the axioms of this logic by using its deduction rules. This result can be used to design a computer system that would automatically check whether a given statement about time intervals is true or not.