Explicitly Defining the Hypothesis Space

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.