Reasoning

Reasoning is the use of logical inference to generate new information.

The ability to reason is of fundamental importance to any intelligent system, as it enables it to use new observations to exceed its original programmed capabilities. There are three kinds of reasoning of particular interest in Artificial Intelligence:

#1 Deductive reasoning

“Given a rule and cause, what is the effect?”

• This determines whether the truth of a conclusion can be determined for a rule, based solely on the truth of the premises. This is useful for prediction.
• Example: “When it rains, things outside get wet. The grass is outside, therefore: when it rains, the grass gets wet.”
• Deduction is truth preserving, if the cause is true, we know the effect with certainty. Induction and Abduction, do not have this property, as the cause and effect only hold for the population of a sample.
• Mathematical logic and programming are based on type of reasoning.

#2 Inductive reasoning

“Given an effect and cause, what is the rule?”

• This attempts to support a determination of the rule. It hypothesizes a rule after numerous examples are taken to be a conclusion that follows from a precondition in terms of such a rule.
• Induction rules don’t necessarily need to be causal, they may be correlations.
• Example: “Every swan I’ve seen is white, therefore: all swans are white” (Though beware excessive generalisation: see the problem of induction)
• Scientific research is an example of this type of reasoning, collecting large amounts of data, then running experiments to test the hypotheses that might explain the data.
• Much of machine learning is also based on the principle of inducing rules from data, by finding those that best fit a data set.

#3 Abductive reasoning

“Given a rule and an effect, what is the cause?”

• This attempts to go from an observation to a theory (a set of premises) which will account for what has been observed, seeking to find the simplest and most likely explanation. Although other explanations may also exist.
• Example: “When it rains, the grass gets wet. The grass is wet. Therefore, it might have rained.”
• Remember, abduction only hints at the cause, as there may be many other reasons for the observed effect. The wet grass might be due to a garden hose.
• Abductive reasoning can be used to develop a hypothesis that can be tested by additional reasoning or data. Hence this approach is well-suited for diagnosticians and detectives.

The three kinds of reasoning complement each other; a rule produced by induction, might later be used deductively or abductively.

For instance, a cognitive system might observe some effects and abduce a explanation, cause and effect can then be used to induce a rule, then once it has rules, it can deduce new effects from causes.

• See also: Reasoning — The Society of Mind, Marvin Minsky