Since ILASP 3.5, the hypothesis space can be defined using ASP. This
can be either completely defined from scratch, or in combination
with mode declarations. This ASP program is passed to ILASP using the
statement #bias("..."), where ... is replaced with the ASP program.
Each answer set of this program is mapped to a rule in the hypothesis
space. This mapping is defined in the rest of this section. Note that
the ASP definition feature replaces the previous (experimental) bias
constraints, which existed in various forms, from ILASP 3.1 to 3.4.
Normal rules and constraints are expressed by answer sets containing the
following predicates: head/1 and body/1. For example, the answer set
{head(p), body(q)} represents the rule p :- q. If the answer set
contains no head atom, then the rule is a constraint.
Negation as failure is represented using the naf/1 function symbol;
for example body(naf(p)) represents that not p is in the body.
Variables are represented using the function symbol var__/1; for
example var__(1) represents the variable V1. So, {
head(p(var__(1)), body(q(var__(1), var__(2), a),
body(q(var__(1), var__(3), b) } represents the rule p(V1) :- q(V1,
V2, a), q(V1, V3, b).
Example.
Consider the following ASP definition of the hypothesis space:
#bias("
1 { head(p); head(q) } 1.
{ body(B) } :- possible_body(B).
possible_body(r).
possible_body(s).
possible_body(naf(s)).
:- body(naf(B)), body(B).
").
If run in ILASP, this will lead to the following hypothesis space being generated:
p.
p :- r.
p :- s.
p :- not s.
p :- r, s.
p :- r, not s.
q.
q :- r.
q :- s.
q :- not s.
q :- r, s.
q :- r, not s.
An answer set representing a choice rule will contain no head/1 atoms,
but will instead contain (potentially multiple) in_head/1 atoms. It
will also contain one lb/1 and one ub/1 atom, specifying the
(integer) lower and upper bound for the choice rule, respectively. For
example, the answer set { lb(0), ub(1), in_head(p), in_head(q), body(r)
} represents the rule 0 { p; q } 1 :- r.
From ILASP 3.6.0, disjunctive rules are supported. Similarly to the case
of a choice rule, an answer set representing a disjunctive rule will
contain no head/1 atoms, but will instead contain (potentially
multiple) in_head/1 atoms. Unlike in the case of a choice rule, it
will not contain the lb/1 and ub/1 atoms. For
example, the answer set { in_head(p), in_head(q), body(r)
} represents the rule p; q :- r.
In order to enable learning disjunctive rules with the default ASP definition of hypothesis spaces (see below), the user must add the following statement to the task:
#bias("allow_disjunction.").
Weak constraints are represented by answer sets using the predicates
weak_body/1, priority/1 and weight/1. For example, the answer set
{ weak_body(p(var__(V1))), weight(1), priority(2) } represents the
weak constraint :~ p(V1).[1@2, V1].
From ILASP 3.6.0, any of the above rules can also include conditional
literals. To represent that a literal lit has a condition c, we use
the atom condition(c, lit). For example, the answer set { in_head(p),
in_head(q), body(r), condition(c_1, p), condition(c_2, p),
condition(c_3, r) } represents the rule p : c_1, c_2; q :- r : c_3.
To specify which predicates can appear in the condition of a conditional
literal using mode declarations, the new #modec declaration should be
used. This is defined in exactly the same way as the #modeb
declarations above.
If a single mode declaration is defined in a task then ILASP will assume
that the default interpretation of mode declarations should be enabled.
This will cause a default ASP program to be used to define the
hypothesis space. You can extend this program by using #bias
statements, but this will only add to the existing program. A common use
of this feature would be to constrain the hypothesis space, for instance
the bias statement #bias(":- body(p(_)), body(q(_)).") states that the
predicates p/1 and q/1 cannot be used together in the body of a rule
in the hypothesis space.
The ASP definition of the hypothesis space (including the representation
of mode declarations) can be seen by running ILASP with the flags -s
and -t together.
In some cases, you may wish to completely disable the default
interpretation of mode declarations. If this is the case, you can add
the flag --override-default-sm. In this case, the ASP definition of
the hypothesis space will consist of the representation of the mode
declarations and whatever ASP rules you have added using bias
statements.