Logike sa metričkim operatorima

The aim of this paper is to combine distance functions and Boolean proposi­ tions by developing a formalism suitable for speaking about distances between Boolean formulas. We introduce and investigate a formal language that is an extension of classical propositional language obtained by adding new binary (modal -like) operators of t he form D≤ s and D≥ s , seQt, Our language all­ ows making formulas such as D≤ s(a , (3 ) with the intended meaning 'distance between formulas a and (3 is less than or equal to s'. The semantics of the proposed language consists of possible worlds with a distanc e function defined between sets of worlds. Our main concern is a complete axiomatization that is sound and strongly complete with respect to the given semantics