Guideline: Boolean logic or algebra

Criteria in rule is true or false. So when combining criteria together to build the condition part of a rule we need to clearly understand the Boolean logic, and its operations.

AND / Conjunction

We will use the following notation the dot as operator for AND so A.B is equivalent to A AND B. The conjunction of two propositions is true when both propositions are true. The truth table is

AND A

True

False

True

True

False

False

False

OR / Disjunction

We use the + operator for A OR B like A + B. Disjunction of two propositions is false when both propositions are false.

OR A

True

False

True

True

False

True

False

NOT / Negation

A	NOT A
True	False
False	True

Implication

A-> B, implication is a binary operation which is false when A is true and B is false. A -> B can be expressed as NOT A OR B.

A -> B A

True

False

True

True

False

False

True

XOR or exclusive OR

Exclusive-or of two propositions is true just when exactly one of the propositions is true

XOR A

True

False

True

False

True

False

True

False

De Morgan's Law

De Morgan's law are rules in formal logic relating pairs of dual logical operators in a systematic manner expressed in terms of negation:

NOT (A AND B) = NOT A OR NOT B

NOT (A OR B) = NOT A AND NOT B

It is important to leverage the De Morgan's law to improve rule writing during the rule transformation.