Inductive Learning of Answer Set Programs

The simplest way to define a hypothesis space is to explicitly define each rule in the space (and the length of each rule).

An explicit definition is of the form:

```
length ~ rule
```

where `length`

is a positive integer and `rule`

is a normal rule, choice
rule, hard constraint or weak constraint. An example of a hypothesis
space expressed in this way is:

```
1 ~ p.
2 ~ p :- r.
2 ~ p :- not s.
3 ~ p :- r, not s.
```

Explicit definitions are the simplest way of defining a hypothesis space; however, in many circumstances, it is not practical to define the hypothesis in this way. For this reason, there are several other, more compact, ways of defining hypothesis spaces in ILASP.