K Modal Logic Approach to Maze Solving

Abstract

This paper presents a modal logic approach to solving maze problem. Traditionally, this problem is solved using graph traversal algorithms, ranging from backtracking and A* to monte-carlo tree search approaches. In this case, we present a novel approach to describing a backtracking algorithm using K modal logic. Modal logic is a powerful way of representing statements that involve some linguistic modalities, e.g. “neces-sary”, “possible”, “was”, “will be”, “permitted”, “forbidden”, etc. This gives new ways to model typical decision making problems. For this purpose, we developed a novel framework called LogicToolbox. We employ this tool in modelling and solving maze problem as an example of a decision making process. We chose to translate a well-known backtracking algorithm to present the expressiveness of the language of modal logic, while proving that solving backtracking as a modal logic problem is equivalent to the backtracking algorithm itself.