It is useful, for certain types of reasoning, to have the things we know about a situation in the form of implications. For instance:

A -> B | A implies B |

of even:

A /\ B /\ C -> D | A and B and C implies D |

### Deduction Using Implies

So if the following are true: - A -> B
- B -> C
- C -> D
then we can deduce: A -> D for example, by combining the implications (substituting). |

### Forward and Backward Chaining

Diagrams, such as the one above, give us a graphical guide.

### As Meet and Join

We may need to express the implication in terms of meet and join ('or' and 'and') . To see how to do this lets look at a truth table for it:

A | B | A->B |

F | F | T |

F | T | T |

T | F | F |

T | T | T |

Note: I've drawn the truth table as Boolean values but we can use constructive logic instead (law of excluded middle not required).