A Prolog application for reasoning on maths puzzles with diagrams

Abstract

ABSTRACT Despite the indisputable progresses of artificial intelligence, some tasks that are rather easy for a human being are still challenging for a machine. An emblematic example is the resolution of mathematical puzzles with diagrams. Sub-symbolical approaches have proven successful in fields like image recognition and natural language processing, but the combination of these techniques into a multimodal approach towards the identification of the puzzle’s answer appears to be a matter of reasoning, more suitable for the application of a symbolic technique. In this work, we employ logic programming to perform spatial reasoning on the puzzle’s diagram and integrate the deriving knowledge into the solving process. Analysing the resolution strategies required by the puzzles of an international competition for humans, we draw the design principles of a Prolog reasoning library, which interacts with image processing software to formulate the puzzle’s constraints. The library integrates the knowledge from different sources, and relies on the Prolog inference engine to provide the answer. This work can be considered as a first step towards the ambitious goal of a machine autonomously solving a problem in a generic context starting from its textual-graphical presentation. An ability that can help potentially every human–machine interaction.