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Backward chaining
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<p>Backward chaining (or backward reasoning) is an <a href="/facts/Inference/RBbe95bP">inference</a> method described colloquially as working backward from the goal. It is used in <a href="/facts/Automated_theorem_prover/vKGvuKFI">automated theorem provers</a>, <a href="/facts/Inference_engine/oLlNX14Q">inference engines</a>, <a href="/facts/Proof_assistant/hjFGxLPn">proof assistants</a>, and other <a href="/facts/Artificial_intelligence/lJGauQwX">artificial intelligence</a> applications. </p><p>In <a href="/facts/Game_theory/zkEIj1ya">game theory</a>, researchers apply it to (simpler) <a href="/facts/Subgame/QoWI377D">subgames</a> to find a solution to the game, in a process called <i><a href="/facts/Backward_induction/x4DwF49D">backward induction</a></i>. In chess, it is called <a href="/facts/Retrograde_analysis/P4QhzkWF">retrograde analysis</a>, and it is used to generate table bases for <a href="/facts/Chess_endgame/ntY8zsJ0">chess endgames</a> for <a href="/facts/Computer_chess/2wE8AU5d">computer chess</a>. </p><p>Backward chaining is implemented in <a href="/facts/Logic_programming/Xgh8lj3F">logic programming</a> by <a href="/facts/SLD_resolution/TlE5h5p0">SLD resolution</a>. Both rules are based on the <a href="/facts/Modus_ponens/Wq4NcmrG">modus ponens</a> inference rule. It is one of the two most commonly used methods of <a href="/facts/Reasoning/tcBImN8J">reasoning</a> with <a href="/facts/Inference_rule/QV5NklQ9">inference rules</a> and <a href="/facts/Logical_consequence/AyDXp4dn">logical implications</a> – the other is <a href="/facts/Forward_chaining/FJjYIf6S">forward chaining</a>. Backward chaining systems usually employ a <a href="/facts/Depth-first_search/luxJKVph">depth-first search</a> strategy, e.g. <a href="/facts/Prolog/r5h66Qh1">Prolog</a>. </p>