Propositional dynamic logic for searching games with errors

We investigate some finitely-valued generalizations of propositional dynamic logic with tests. We start by introducing the n+1n+1-valued Kripke models and a corresponding language based on a modal extension of Łukasiewicz many-valued logic. We illustrate the definitions by providing a framework for an analysis of the Rényi–Ulam searching game with errors.Our main result is the axiomatization of the theory of the n+1n+1-valued Kripke models. This result is obtained through filtration of the canonical model of the smallest n+1n+1-valued propositional dynamic logic.