A Propositional Logic with Binary Metric Operators.

The aim of this paper is to combine distance functions and Boolean propositions 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 the form D⩽s and D⩾s, s ∈ Q+ 0. Our language allows making formulas such as 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. Our main concern is a complete axiomatization that is sound and strongly complete with respect to the given semantics.

Authors

• Nenad Stojanovic
• Nebojsa Ikodinovic
• Radosav Djordjevic

Keywords

• metric operators
• soundness
• completeness