Logical Calculi for Knowledge Discovery in Databases Jan Rauch Laboratory of Intelligent Systems, Faculty of Informatics and Statistics, University of Economics, W. Churchill Sq. 4, 13067 Prague, Czech Republic Abstract. Observational calculi were defined in relation to GUHA met- hod of mechanising hypotheses formation. Formulae of observational cal- culi correspond to statistical hypothesis tests and various further asser- tions verificated in the process of data analysis. An example of appli- cation of the GUHA procedure PC-ASSOC is described in the paper. Logical relation among formulae of observational calculi are discussed and some important results concerning deduction rules are shown. Pos- sibilities of applications of logical properties of formulae corresponding to hypotheses tests in the field of KDD are suggested. 1 Introduction The goal of this paper is to introduce special logical calculi as a useful tool for Knowledge Discovery in Databases (KDD). We start with the following two facts: - Each database can be understood as a formally described data structure. We refer to a fact that particular relations and fields have their own names. l~esults of methods of data mining are assertions dealing with these names. Assertions are in various form, e.g. association rules [1], results of statistical hypotheses tests or presentation graphs. Anyway, each such assertion can be understood as a formal expression concerning a formal data structure. - Mathematical logic studies formal languages and formal data structures as their models. It is defined what does it mean that a sentence of formal lan- guage is true/false in a model. A very known example is first-order predicate calculus. There is lot of interesting results concerning universally valid for- mulas, deduction rules, an axiomatization, a decidability, etc. see e.g. [6]. We are going to argue that some of these logical concepts are or ,could be useful from the point of view of KDD. a) Observational calculi were defined and studied in relation to GUHA methods of mechanising hypotheses formation [2]. GUHA is a method of exploratory data analysis and it is also successfully used as a method of KDD [10]. The goal of GUHA method is to offer all interesting facts following from the analysed data to the given problem. GUHA is realised by GUHA-procedures. GUHA-procedure is a computer program, the input of which consists of the