Decision list

Decision lists are a representation for Boolean functions which can be easily learnable from examples. 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 language specified by a k-length decision list includes as a subset the language specified by a k-depth decision tree.

Learning decision lists can be used for attribute efficient learning.

Definition
A decision list (DL) of length $r$ is of the form:

if $f_{1}$ then output $b_{1}$ else if $f_{2}$ then output $b_{2}$ ... else if $f_{r}$ then output $b_{r}$

where $f_{i}$ is the $i$th formula and $b_{i}$ is the $i$th boolean for $$i \in \{1...r\}$$. The last if-then-else is the default case, which means formula $f_{r}$ 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.