 For the semantic interpretation, a relation \(R_\alpha\) is required for each program \(\alpha\). However, while the relations \(R_a\) for basic programs are arbitrary, those for complex programs should behave according to their intended meaning. The simplest way to obtain this is to take the relations for the basic programs, and then define those for complex programs in an inductive way. This and further details about PDL can be found in Troquard and Balbiani (2019:  [Section 2).