Implication : A survey of the different logical analyses of 'if ..., then ...'

This paper discusses different forms of implication as they are used in logic, mathematics, linguistics and artificial intelligence. The most commonly used form is that of material implication. It has turned out, however, -- as the paper makes clear -- that there are aspects that are not covered by this material implication. This has led to strict implication (in order to provide for necessity) and relevant implication (for relevance). There are still other forms of implication. The paper discusses counterfactuals and intuitionistic implication. Finally, a survey is given of decision procedures for different kinds of implication.

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