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A Propositional Metric Logic with Fixed Finite Ranges

Djordjević Radosav, Ikodinović Nebojša, Stojanović Nenad

Fundamenta Informaticae

2020

Vol. 174, nr 2

185--199

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.