Backward Chaining:
In generally given that we are only interested in constructing the path whether we can set our initial state to be the theorem statement and search backwards until we find an axiom or set of axioms. There if we restrict ourselves to just utilising equivalences as rewrite rules for this approach is OK, is just because we can use equivalences both ways, and any path from the theorem to axioms that is found will provide a proof. In fact, if we use inference rules to traverse from theorem to axioms like we will have proved that and if the theorem is true then the axioms are true. Whether we already know that the axioms are true! Just to get around this we must invert our inference rules and try to work backwards. Means that, the operators in the search basically answer the question: as what could be true in order to infer the state like logical sentence we are at right now? In the Arch space if we set our agent starts searching from the theorem statement and reaches the axioms, than it has proved the theorem. In fact this is also problematic means there are numerous answers to the inversion question so and the search space gets very large.