Quantitative Modalities, Possible Applications to Information Analysis

Abstract

The paper formalizes quantitative (numerical) modalities and describes their possible applications. We work via standard Kripke-like semantics for modal logics and introduce quantitative modalities as possibility to have predefined amount of different states (worlds) where formulas may be valid. Approach is applied to various modal semantics with distinct requirements to the accessibility relations (as e.g. to be reflexive, transitive). We illustrate possible applications in internet search, trading, banking transfers and another interference in internet network or another communication in information channels. Basic attention (as to mathematical subject) is directed to basic algorithmic problems - satisfiability and decidability problems, we find resolving algorithms. That is done for modal logic with quantitative modalities and for temporal logics generated by these quantitative modal logics by consideration temporal operations as bi-modalities. We conclude the paper with pointing open problems and possible further directions in research.