Abschlussarbeit

Beschreibung:

Modal logic examines reasoning that incorporates expressions like ”necessarily” and ”possibly.” However, the term ”modal logic” is often used more broadly to encompass a family of related logics that follow similar principles but utilize different symbols and rules. It is used often in Multi-Agent Systems, and game theory.

One of the critical challenges in Artificial Intelligence (AI) is managing contradictory information. When data is aggregated from multiple sources, inconsistencies often arise, necessitating a structured approach to measure and address these contradictions. In propositional logic, inconsistency measures [1, 3] have been developed to quantitatively assess the impact of such conflicts on knowledge bases. However, these measures are largely unexplored in the context of modal logic.

This thesis aims to adapt existing inconsistency measures from propositional logic, in addition to those based on hitting sets [2], for application in modal logic. The study will involve modifying the measures to align with the possible world semantics of modal logic, analyzing their properties, and evaluating their compliance with established inconsistency measure postulates [2]. Furthermore, the establishment of rationality postulates appropriate for modal logic. The outcome of this research could provide valuable insights into handling inconsistencies in modal logic domains, offering a foundation for future advancements in reasoning and representing inconsistent knowledge in modal logic.

References

[1] John Grant and Maria Vanina Martinez, editors. Measuring Inconsistency in Information. College Publications, [London], 2018.

[2] Matthias Thimm. On the compliance of rationality postulates for inconsistency measures: A more or less complete picture. Künstliche Intelligenz, 31(1):31–39, March 2017.

[3] Matthias Thimm. On the evaluation of inconsistency measures. In John Grant and Maria Vanina Martinez, editors, Measuring Inconsistency in Information, volume 73 of Studies in Logic. College Publications, February 2018.