Classes of four-fold table quantifiers

Abstract

Abstract. Four-fold table logical calculi are defined. Formulae of these calculi correspond to patterns based on four-fold contingency tables of two Boolean attributes. An FFT quantifier is a part of the formula, it corresponds to an assertion concerning frequencies from four-fold table. Several classes of FFT quantifiers are defined and studied. It is shown that each particular class has interesting properties from the point of view of KDD. Deduction rules concerning formulae of four-fold tables calculi are demonstrated. It is shown that complex computation of statistical tests can be avoided by using tables of critical frequencies.

Combining implicational quantifiers for equivalence ones by fuzzy connectives

“…Properties of basic quantifiers are in the core of the general definition of several useful classes of quantifiers 1,7 …”

“…We concentrate to the most widely used observational quantifiers, called in Ref. 7 fourfold table quantifiers. So far these quantifiers were treated in classical logic as 0/1-truth functions.…”

On the Correspondence between Classes of Implicational and Equivalence Quantifiers

“…Properties of basic quantifiers are in the core of the general definition of several useful classes of quantifiers [4], [5], [11]:…”

“…in the systems PC-GUHA [6], Knowledge Explorer [3], and 4FT-Miner [12]. Further investigations of its mathematical and logical foundations are going on nowadays [7], [10], [11]. We concentrate to the most widely used observational quantifiers, called in [11] four-fold table quantifiers.…”

“…Further investigations of its mathematical and logical foundations are going on nowadays [7], [10], [11]. We concentrate to the most widely used observational quantifiers, called in [11] four-fold table quantifiers. So far this quantifiers were treated in classical logic as 0/1-truth functions.…”