Forward Chaining - Artificial intelligence:

Imagine we have a set of axioms which we know are true statements regarding the world. If we set these to each be a starting state of the search space and we set the aim state to be our theorem statement, then it is a simple approach which may be used to prove theorems. We call this approach forward chaining approach because the agent employing the search constructs chains of reasoning from the axioms, positively to the goal. Once a path has been found from the axioms to the theorem, this is the path to constitutes a proof and the problem has been solved.

However,in general, the problem with forward chaining is that it cannot easily use the goal (theorem statement) to drive the search. Hence it actually might just explore the search space until it comes across the solution. Goal-directed searches are frequently more effective than non-goal directed ones like forward chaining.