When enough information is available, we use deductive reasoning. In cases where we have incomplete information (as is usually the case in the real world), we must use some form of inductive or plausible reasoning. But which sort?
Certainty Factors Confirmation Theory Criteria estimators Dempster-Shafer theory Endorsements Fuzzy Logic Higher order Imprecise probabilities Likelihood Neyman-Pearson Odds Possibility theory Probability Rough Sets
A note on terminology
To form a judgement about the likely truth or falsity of any proposition A,
the correct procedure is to calculate the probability that A is true conditional on all the evidence at hand:
P(A|E1, E2,...)
The vertical bar '|' means 'given' (so that all items to the right of this conditioning symbol are taken as being true).
There is no such thing as an absolute probability.
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BayesianBayesians condition on the data actually observed and consider the probability distribution on the hypotheses; they believe it reasonable to put probability distributions on hypotheses and they behave accordingly.P(hypothesis|data, background information) |
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FrequentistFrequentists condition on a hypothesis of choice and consider the probability distribution on the data, whether observed or not.P(data|null hypothesis) |
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Fuzzy LogicFuzzy terminology would be, for example, truth("Drew is TALL") = 0.38 (see comp.ai.fuzzy newsgroup FAQ).P(a person would agree with the hypothesis|data, the person is a competent speaker of the language and given the options of "agree" or "disagree") |
LikelihoodThe likelihood, L(hypothesis|data), of the hypothesis given the data is proportional to P(data|hypothesis)P(data|hypothesis, background information)/P(data|background information) = constant × P(data|hypothesis) |