Dismath: Discrete Math Gamified Educational Tool in Logic with Minimax Algorithm and Pruning

摘要

This paper presents the design and development of Dismath, a gamified educational tool for propositional logic introduction to undergraduate computer engineering students. Additionally, an artificial intelligence (AI) agent is developed for the proposed Dismath game based on minimax tree search with alpha-beta pruning (MMAB). Dismath is an international checker variant inspired by Damath game in which operations are defined in every checkerboard positions. Thus, the final score is not only dependent on the pieces left but also in the operation results. In a capture move, the jumping chip is the first operand, the captured piece acts as the second operand, and the operation defined in the destination block where the chip landed after the jump is utilized for the binary operation. Instead of arithmetic operators, Dismath designates logical connectives on the checkerboard. All white and black pieces were assigned true and false truth values. For scoring, a true (T) and a false (F) truth values are calculated as +1 and -1, while a dama or king chip is valued +2 and -2 for White and Black pieces, respectively. If the game ends with a positive value, then white wins; otherwise black wins, unless the score is zero in which the outcome is draw. Board balancing experiments were conducted using the win-win ratio between the two random players as evaluation metric. Furthermore, the MMAB agent was characterized against a random player baseline. The results showed dominant performance of MMAB AI agent in proposed Dismath game losing only at depth equal to 1. Overall, this result is promising on its own demonstrating the automated gameplay of the proposed Dismath educational tool for logic introduction.