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Deduction rules

The deduction rule in the logical calculus of association rules is a relation of the form

Deduction rule

where α1, α2, , αn, β are association rules. This deduction rule is correct if it holds for each data matrix M: If α1, α2, , αn are true in M, then also β is true in M.

We are interested in correct deduction rules of the form

Correct deduction rule

where φ ψ and φ' ψ' are association rules.

Such deduction rules can be used namely in the following ways:

Thus it is reasonable to ask when the deduction rule of the form

Correct deduction rule

is correct. It can shown that there are several propositional formulas Φ, Ψ derived from φ, ψ, φ', ψ' such that this deduction rule is correct if and only if Φ and Ψ are tautologie of the propositional calculu [Ra 98A], [Ra 98C]. The propositiobnal formulas Φ, Ψ depends on the class of 4ft-quantifiers the quantifier belongs to.

Some of these deduction rules are applied in the procedure 4ft-Miner.

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