Transitive Logic

ISM is based on the mathematical concept of Transitive Logic. This concept is used to reduce the number of comparisons (and thus time) needed to construct the ISM. Transitive Logic is also used to simplify the topology of the visual model. Transitive Logic states that for any 3 elements (A, B, C) with a given relation (à) when:

• A has the relation to B, (written A*B),
• And B has the relation to C, (written B*C),
• Then A has the relation to C, (written A*C or A*B*C).

• If travel by car is faster than travel by bicycle,
• And travel by bicycle is faster than travel by walking,
• Then travel by car is faster than travel by walking.

• A has the relation to B,
• And A does not have the relation to D,
• Then B does not have the relation to D. (B cannot have the relation to D or, using transitive logic, A would have to have the relation to D also.)

• If travel by car is faster than travel by bicycle,
• And travel by car is not faster than travel by airplane,
• Then travel by bicycle is not faster than travel by airplane.

• If a cat is a kind of animal,
• And a cat is not a kind of dog,
• Then an animal is not a kind of dog. (But a dog may still be a kind of animal).

Concept Star software uses this type of logic to infer some of the relationships, based on answers already given by the user. The number of inferred answers in an ISM session will vary with the situation, but it is often in the order of 70% . This represents considerable time saving for practical use of ISM.

For more information about how Concept Star works click Concept Star basics.

Concept Star decision support system is easy to learn & use. Concept Star professional software and training package is reasonably priced and includes all materials needed to learn and use Concept Star effectively.