Decision lists are a representation for Boolean functions which can be easily learnable from examples.
[1] Single term decision lists are more expressive than disjunctions and conjunctions; however, 1-term decision lists are less expressive than the general disjunctive normal form and the conjunctive normal form.
The last if-then-else is the default case, which means formula fr is always equal to true.
A k-DL is a decision list where all of formulas have at most k terms.
Sometimes "decision list" is used to refer to a 1-DL, where all of the formulas are either a variable or its negation.