 In addition to the unary \(\mathsf{HS}\) interval modalities associated with Allen’s binary interval relations, there is a natural and important operation of chopping an interval into two subintervals, which gives rise to the ternary interval relation ‘chop’, proposed and studied in Moszkowski (1983). The framework was later extended in Venema (1991) to the logic CDT, which involves next to ‘chop’ (\(C\)), the two residual ‘chop’ operators \(D\) and \(T.\) The logic CDT was completely axiomatized in Venema (1991); see also Goranko et al. (2004) and Konur (2013).