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The classes of association rules are defined by classes of 4ft quantifiers. There are various classes of 4ft-quantifies defined already in [Ha 78], e.g. implicational quantifiers and associational quantifiers. Further classes of 4ft-quantifiers are defined e.g. in [Ra 98A] and [Ra 98C].

Classes of 4ft-quantifiers can be defined using TPC – truth
preservation condition. An example of TPC is a truth preservation condition
TPC_{⇒} for implicational
quantifiers:

TPC_{⇒}:
a' ≥ a
∧ b'
≤ b.

The TPC_{⇒} is used in the
definition of implication quantifier such in the following way:

The 4ft quantifier ≈ is implicational if for all quadruples 〈a,b,c,d〉 and 〈a',b',c',d'〉 of integer non-negative numbers such that a + b + c + d > 0 and a + b + c + d > 0 the following is satisfied:

If ≈(a,b,c,d) = 1 and a' ≥ a ∧ b' ≤ b then also ≈(a,b,c,d) = 1.

The following quantifiers implemented in the 4ft-Miner procedure are
implicational:
founded implication ⇒_{p, Base},
lower critical implication ⇒^{!}_{p,
αBase} and
upper critical implication ⇒^{?}_{p,
αBase}.

Double implicational quantifiers, ∑-double implicational quantifiers and furthers classes of 4ft-quantifiers are defined and studied e.g. in [Ra 98A] and [Ra 98C], see also [Bu 03].

There are interesting results related to defined classes of association rules – see e.g. deduction rules and some further properties of association rules.

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