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An Isaac Newton Institute Workshop

Logic and Databases

Approximation Logic and Databases

Author: Michael Katz (Haifa University)

Abstract

The Logic of Approximation is an infinite-valued first order logic, designed to handle inexactness in scientific research. Truth-values of this logic, ranging in the closed interval [0,1], are 'degrees of error'. Thus 0 (no error) stands for absolute truth and 1 (maximal error) for absolute falsehood. The semantic rules for connectives and quantifiers are reversals of familiar rules of fuzzy logics. Unique to this logic is a notion of deduction based on the idea that errors in the conclusion can be minimized (to within arbitrary epsilon) if errors in the premiss are controlled (to within appropriate delta). In the past this logic was developed and applied by the author to geometry, quantum theory, measurement theory and utility theory. In the present paper it is to be applied to the study of relational databases. In particular we shall try to show how to handle, within the framework of the logic of approximation, various properties of specific databases derived from batteries of intelligence tests and from surveys of social attitudes.