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

where α_{1},
α_{2},
…,
α_{n},
β are association rules. This deduction rule is
correct if it holds for each data matrix `M`: If
α_{1},
α_{2},
…,
α_{n} are true in `M`, then also
β is true in `M`.

We are interested in correct deduction rules of the form

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

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

*To reduce the output of a data mining procedure:*If the association rule φ ≈ ψ is a part of a data mining procedure output (i.e. it is true in an analysed data matrix) and ifis the correct deduction rule then it is not necessary to put the association rule φ' ≈ ψ' into the output. The used deduction rule must be transparent enough from the point of view of the user of the data mining procedure. An example of a simple deduction rule is a dereduction deduction rule

that is correct for each implicational quantifier ⇒* [Ha 78].

*To decrease the number of actually tested association rules:*If the association rule φ ≈ ψ is true in the analysed data matrix and ifis the correct deduction rule, then it is not necessary to test φ' ≈ ψ'.

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

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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