Affiliations: [a] Faculty of Science, University of Kragujevac, 34000 Kragujevac, Serbia. [email protected] | [b] Faculty of Mathematics, University of Belgrade, 11000 Belgrade, Serbia. [email protected] | [c] Faculty of Science, University of Kragujevac, 34000 Kragujevac, Serbia. [email protected]
Correspondence:
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Address for correspondence: Faculty of Science, University of Kragujevac, 34000 Kragujevac, Serbia
Abstract: The aim of this article is developing a formal system suitable for reasoning about the distance between propositional formulas. We introduce and study a formal language which is the extension of the classical propositional language obtained by adding new binary operators D≤s and D≥s, s ∈ Range, where Range is a fixed finite set. In our language it is allowed to make formulas of the form D≤s(α; β) with the intended meaning ’distance between formulas α and β is less than or equal to s’. The semantics of the proposed language consists of possible worlds with a distance function defined between sets of worlds.
