On information functions. Part One : Basic formal properties

Abstract

In this paper we present the definition and fundamental properties of the information functions - functions which establish a correspondence between sets of formulas and information contained in these sets. The intuitions of the notion of information stem from Bar-Hillel-Carnap's conception derived from [1]. The information contained in the proposition is, according to this conception, the set of all state-descriptions excluded by this proposition. By S we shall note the set of all formulas in the language {—, A, V, —)• and by C, the classical consequence operation over S. Instead of C(0) we write T aut. The set of all complete subsets of S we note as Cpl. We put forward the following definition (Fragment tekstu).