Declarative Modelling and Reasoning for Combinatorial Problem Solving and Argumentation under Uncertainty

This thesis develops new declarative modelling and reasoning techniques for combinatorial mathematical word problems and argumentation under uncertainty. The first set of contributions regards combinatorial mathematical word problems, which ask to count the number of possible configurations of a setting sketched in natural language. They represent an interesting challenge for AI because they are often used as a benchmark for human cognition. The first contribution is the identification of key aspects of combinatorics math problems which traditional declarative frameworks fail to support adequately, thus preventing an appropriate modelling. Second, we address these limitations proposing a novel declarative language for modelling combinatorics math problems. Third, we pair the contributions to modelling with novel reasoning techniques for combinatorics math problems and we implement them in a solver tested on both real-world and artificial examples. The second set of contributions of this thesis is related to argumentation, which is the task of structuring and determining the acceptability of arguments in a debate. Designing systems that are able to argue and persuade is a very relevant and challenging AI task, and taking into account uncertainty is fundamental in such situations. The first contribution is a novel modelling approach to argumentation under uncertainty based on probabilistic logic programming (PLP), a popular declarative framework for modelling and reasoning about structured, uncertain domains. Second, we introduce novel reasoning techniques to solve such problems, because the logic component of traditional PLP frameworks is too restricted to reason over such models. Third, we show that modelling argumentation problems with PLP gives them access to the general purpose tools and algorithms of PLP for reasoning and learning under uncertainty.

Jaar van publicatie:2023

Toegankelijkheid:Open