Backward reasoning

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Backward reasoning (or goal-oriented inference) is an inference method used in artificial intelligence. Given an implication "if A then B", it reasons "backwards" from the goal of establishing B to the sub-goal of establishing A. In contrast, given both A and the same implication, forward reasoning, also called modus ponens, derives the conclusion B. Backward reasoning is implemented in logic programming by SLD resolution.

Employing backward reasoning to infer a cause from an effect carries a number of difficulties. The most obvious is that many effects can have multiple causes. An example often used is the observation that the street is wet. If it is known that the street can become wet from rain, backward reasoning can abduce that it has recently rained. Clearly this is not the only inference that can be made. The street might have been wetted by a street cleaning machine, a leaking water supply, or many other causes. Only in the unusual cases where an effect occurs IF and only IF (IFF) a single cause has previously occurred is the initial inference from backward reasoning justified. Otherwise, additional information is required to discard potential causes until only one remains.

This process is a staple of crime fiction, where the investigator is faced with an effect (the crime) for which there are a number of possible causes (suspects). Sir Arthur Conan Doyle's creation Sherlock Holmes, arguably fiction's most famous detective, put it this way:

"When one has eliminated the impossible whatever is left, however improbable, must be the truth."

[edit] Example

Given the implication "If You have a fever or a sneezing fit or a chill, then you have a cold", backward reasoning uses the implication to show that you have a cold by attempting to show that you have a fever or a sneezing fit or a chill.