Rules

Overview

In logic programming, rules define how new facts can be inferred from existing ones. These rules are called implications because they specify the conditions under which a certain fact holds based on other known facts.

A rule follows this general format:

<conclusion> :- <condition>;

• The head (on the left of :- ) represents the conclusion—the new fact being inferred.
• The body (on the right of :- ) lists the conditions that must be met for the conclusion to hold.

TIP

:- sign is called implication symbol.

This syntax is read as:

The conclusion holds if the conditions in the body hold.

Rules in Logica are built by combining predicate calls through two 2 fundamental logic operators:

• Conjunction denoted as , which stands for logical AND.
• Disjunction denoted as | which stands for logical OR.

Example Rules

Example 1: To state "X is a quadruped if it has 4 legs" in Logica, we would write:

Quadruped(x) :- NumLegs(x, 4);

The body of this rule is a single call to pre-existing NumLegs predicate.

Example 2: To state "X is the grandparent of Z if X is the parent of the parent of Z" in Logica, we would write:

Grandparent(x, z) :- Parent(x, y), Parent(y, z);

The body of this rule is a conjunction of calls to pre-existing Parent predicate.

TIP

Logica uses , to indicate "AND"

Example 3: X is a sibling of Y if they are children of the same parent.

Sibling(x, y) :- Parent(z, x), Parent(z, y);

Example 4: X is a very close relative of Y if X is a parent of Y or Y is a parent of X.

VeryCloseRelative(x, y) :- Parent(x, y) | Parent(y, x);

The body of this rule is a disjunction of calls to pre-existing Parent predicate.

TIP

Logica uses | to indicate "OR"

Example 5: X is a close relative of Y if X is a parent, a child, or a sibling of Y.

CloseRelative(x, y) :-
  Parent(x, y) |
  Parent(y, x) |
  (Parent(z, x), Parent(z, y));

Multiple rules for a predicate are also allowed. This means that you can define a predicate with several rules, and it is equivalent to a single rule whose body is the disjunction (logical OR) of the bodies of those rules.

Example 6: Equivalent to Example 4. "X is a close relative of Y if X is the parent of Y. X is a close relative of Y if X is the child of Y. X is a close relative of Y if X is a sibling of Y."

CloseRelative(x, y) :- Parent(x, y);
CloseRelative(x, y) :- Parent(y, x);
CloseRelative(x, y) :- Parent(z, x), Parent(z, y);

Alternative Rule Formats

The base format for rules in Logica is <conclusion> :- <condition>;. However, Logica also supports additional rule formats, which will be introduced and explained on a case-by-case basis.