Backward Chaining - Artificial intelligence

Given that we are just interested in constructing the path, we may set our initial state to be the theorem statement and search backwards until we find an axiom (or set of axioms). If we limited ourselves to only using equivalences as rewrite rules, then this approach is OK, because we may use equivalences in both ways, and any path from the theorem to axioms which is found will provide evidence. However, if we use inference rules to traverse from theorem to axioms, then we will have shown (proved) that, if the theorem is true, then the axioms are true. But already we know that the axioms are true. To get around this, we might invert our inference rules and try to work backwards. That is, the operators in the search really answer the question: what could be true in order to infer the state (logical sentence) we are at right now?

If our agent begins searching from the theorem statement and reaches the axioms, it has proved the theorem.  It is also problematic, because there are several answers to the inversion question, and the search space gets very high.