Classes of Four-Fold Table Quantifiers Jan Rauch Laboratory of Intelligent Systems, Faculty of Informatics and Statistics, University of Economics, W. Churchill Sq. 4, 13067 Prague, Czech Republic rauch@vse.cz 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 sta- tistical tests can be avoided by using tables of critical frequencies. 1 Introduction Interesting patterns - assertions concerning analyzed database are the the core of KDD process . Some of these assertions can be easily understood as formulae of a suitable logical calculus. Names of relations and names of fields of the analyzed database belong to basic symbols of such calculus. There are interesting and useful features of these calculi, e.g., deduction rules [7]. There is a group of important patterns concerning two Boolean attributes derived from the analyzed database. The patterns correspond to the relations of the Boolean attributes. The patterns are evaluated on the basis of a four-fold table Tab.1. Here ~o and r are attributes, a is the number of objects (records of the analyzed database) satisfying both ~o and r b is the number of objects satisfying ~o and not satisfying r etc. r -,r c d Table 1. Four-fold table of ~0 and r An example of a pattern based on the four-fold table is the association rule, see [1]. Attributes ~o and r with four-fold table (a, b, c, d) are associated by an association rule with parameters conf and sup if and only if a a >conf A >sup. a+b- a+b+c+d-