Negation

Negation is a fundamental concept in logic programming, serving as a tool to exclude unwanted facts or to set conditions. After understanding aggregation in Logica, we can gain a clearer insight into how negation operates within Logica.

In Logica, Negation as an aggregating expression. To negate a proposition, use the ~ operator, which functions as an aggregating expression. Consider the following set of facts:

Bird("sparrow");
Bird("eagle");
Bird("canary");
Bird("cassowary");

CanFly("sparrow");
CanFly("eagle");
CanFly("canary");

CanSing("sparrow");
CanSing("canary");
CanSing("cassowary");

Suppose we want to identify all birds that can sing but cannot fly. This can be achieved with the following rule:

InterestingBird(x) :-
  Bird(x), CanSing(x), ~CanFly(x);

Logica interprets the negation in this rule as follows:

InterestingBird(x) :-
  Bird(x), CanSing(x), Max{1 :- CanFly(x)} is null;

The aggregating expression Max{1 :- CanFly(x)} will aggregate over a non-empty multiset of 1 values if and only if the proposition CanFly(x) holds. Otherwise, it will aggregate over an empty set, resulting in null.

NOTE

An observant reader may note that any other built-in aggregating operator could be used here. For example, Sum{42 :- CanFly(x)} would yield the same result.

Negation ​

Negation