When probability meets logic

• Main Author: Chan, Jared Nathaniel Weng Wai
• Other Authors: Fan Xiuyi
• Format: Final Year Project
• Language: English
• Published: Nanyang Technological University 2024
• Subjects: Computer and Information Science; Probabilistic assumption-based argumentation
• Online Access: https://hdl.handle.net/10356/175301
• Institution: Nanyang Technological University

This paper explores the application and enhancement of formal languages in artificial intelligence systems to simulate human-like reasoning and problem-solving capabilities. Specifically, it delves into Assumption-based Argumentation (ABA) and its probabilistic extension, Probabilistic Assumption-based Argumentation (PABA), illustrating their roles in non-monotonic reasoning, game theory, and legal dispute resolution. Acknowledging the inherent uncertainties in these systems, such as measurement errors, the study emphasises the integration of probabilistic rules to better mirror the real-world complexities. A significant focus is placed on employing optimization techniques within these reasoning methodologies, despite the potential vastness of the feasible solution space. The paper advocates for the Principle of Maximum Entropy as a guiding principle to identify optimal distributions that maximise uncertainty without introducing unnecessary assumptions, ensuring an unbiased inference process. However, the approach is challenged by exponential space complexity and the management of large matrices. To address these issues, this study proposes a solution that not only locally maximises entropy but also tackles the computational challenges, aiming to enhance the efficiency and applicability of formal languages in AI reasoning processes.