Backward chaining

Backward chaining (or backward reasoning) is an inference method described colloquially as working backward from the goal. It is used in automated theorem provers, inference engines, proof assistants, and other artificial intelligence applications. In game theory, researchers apply it to (simpler) subgames to find a solution to the game, in a process called backward induction. In chess, it is called retrograde analysis, and it is used to generate table bases for chess endgames for computer chess. Backward chaining is implemented in logic programming by SLD resolution. Both rules are based on the modus ponens inference rule. It is one of the two most commonly used methods of reasoning with inference rules and logical implications – the other is forward chaining. Backward chaining systems usually employ a depth-first search strategy, e.g. Prolog. Backward chaining starts with a list of goals (or a hypothesis) and works backwards from the consequent to the antecedent to see if any data supports any of these consequents. An inference engine using backward chaining would search the inference rules until it finds one with a consequent (Then clause) that matches a desired goal. If the antecedent (If clause) of that rule is not known to be true, then it is added to the list of goals (for one's goal to be confirmed one must also provide data that confirms this new rule). For example, suppose a new pet, Fritz, is delivered in an opaque box along with two facts about Fritz: Fritz croaks Fritz eats flies The goal is to decide whether Fritz is green, based on a rule base containing the following four rules: If X croaks and X eats flies – Then X is a frog If X chirps and X sings – Then X is a canary If X is a frog – Then X is green If X is a canary – Then X is yellow With backward reasoning, an inference engine can determine whether Fritz is green in four steps. To start, the query is phrased as a goal assertion that is to be proven: "Fritz is green". 1.