Editing Inductive logic programming (section)

=== Learning from interpretations ===
In learning from interpretations, the ''positive'' and ''negative'' examples are given as a set of complete or partial [[Herbrand structure]]s, each of which are themselves a finite set of ground literals. Such a structure ''{{mvar|e}}'' is said to be a model of the set of clauses <math display="inline">B \cup H</math> if for any [[Substitution (logic)|substitution]] <math display="inline">\theta</math> and any clause <math display="inline">\mathrm{head} \leftarrow \mathrm{body}</math> in <math display="inline">B \cup H</math> such that <math display="inline">\mathrm{body}\theta \subseteq e</math>, <math>\mathrm{head}\theta \subseteq e</math> also holds. The goal is then to output a hypothesis that is ''complete,'' meaning every positive example is a model of  <math display="inline">B \cup H</math>, and ''consistent,'' meaning that no negative example is a model of <math display="inline">B \cup H</math>.<ref name="setting" />