Formal Approach to Information Uncertainty Modelling and Domain Adequacy in DIS Ontologies

Abstract

Ontologies play a central role in structuring domain knowledge and enabling automated reasoning within a given domain. However, real-world applications increasingly demand ontologies that can tolerate and represent uncertainty, stemming from either imperfect information or a mismatch between the ontology and its intended domain. This thesis addresses two fundamental types of ontological uncertainty: (1) uncertainty due to information imperfections, such as incompleteness and ambiguity; and (2) uncertainty of relevance, which arises when ontologies fail to capture the semantics of their domain adequately. To address these challenges, this thesis makes four key contributions. First, it presents a comprehensive survey and classification of uncertainty modelling approaches in domain ontologies, synthesizing a decade of research (2010-2024). It then proposes a formal taxonomy that links types of uncertainty with their appropriate mathematical formalisms for management, and their points of occurrence within the ontologies. Second, it proposes a possibilistic extension to the Domain Information System (DIS) framework that incorporates necessity-weighted formulas to model incomplete information and support flexible, logic-based reasoning. Third, it introduces a novel theory of domain adequacy, based on formal notions of ontological and data commitments, to guide the construction of minimal yet semantically sufficient sub-ontologies. Fourth, it extends this theory to statically defined datascape concepts, developing a practical framework and tooling that enables automated validation of data adequacy through statistical evaluation of real-world datasets. Altogether, this work advances the theoretical foundation and practical implementation of uncertainty-aware ontology engineering. It demonstrates how to unify data- centric reasoning with formal ontology design, yielding systems that are not only semantically rigorous but also grounded in empirical evidence. The results offer a principled approach to managing uncertainty in ontology-based systems, making them more adaptable, interpretable, and aligned with dynamic, data-driven domains.