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|
|A /\ B /\ C -> D||A and B and C implies D|
Deduction Using Implies
So if the following are true:
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:
Note: I've drawn the truth table as Boolean values but we can use constructive logic instead (law of excluded middle not required).