Observational Calculi - Tool for Semantic Web

The goal of this poster is to draw attention to observational calculi, to explain their main features and to outline possibilities of their application in Semantic Web. Observational calculi were defined in the book [1] as a tool to answer the questions (i) Can computers formulate and verify scientific hypotheses? (ii) Can computers in a rational way analyze empirical data and produce a reasonable reflection of the observed empirical world? Can it be done using mathematical logic and statistics? Formulas of observational calculi correspond to suitable statements concerning observational data. The important observational calculi studied in [1] are observational predicate calculi. They are defined by modifications of predicate calculi. The modifications consist in allowing only finite models (that correspond to analyzed data in the form of {0,1} data matrices) and in adding generalized quantifiers. The generalized quantifiers are used to express patterns corresponding to statistical hypothesis tests. Important theoretical results concerning logic of observational calculi are published in [1]. Observational calculi are also studied in relation to data mining [3]. There are important new results concerning logic of association rules [4] enhancing results achieved in [1]. The association rule is understood as an expression φ ≈ ψ where φ and ψ are Boolean attributes derived from columns of an analyzed data matrix. Intuitive meaning of the rule φ ≈ ψ is that Boolean attributes φ and ψ are associated in the way corresponding to the symbol ≈. The symbol ≈ is called the 4ft-quantifier. It is associated to a condition concerning a four-fold contingency table of φ and ψ in the analyzed data matrix. This condition corresponds e.g to χ-test or it can in a simple way express various types of relations (implication, equivalence) between φ and ψ. There are both theoretically interesting and practically important results concerning logic of association rules [1, 4]. An example is a criterion of correctness of deduction rules of the form φ≈ψ φ′≈ψ′ where φ ≈ ψ and φ′ ≈ ψ′ are association rules [4]. Possibilities of applications of observational calculi in Semantic Web are related to analytical reports presenting results of data mining. The process of data mining usually starts by an analytical question. An answer to such question can be an analytical report. For the given question there is a well defined structure of the corresponding analytical report. The structure is described by chapters and sections and must fit to the solved problem and to the accepted domain knowledge. The core of each section are patterns found in analyzed data [3, 5].