Formal Concept Analysis (FCA) is a mathematical framework widely used in Knowledge Representation and Reasoning to study conceptual hierarchies. In FCA, concepts are represented as pairs of objects and features, corresponding to the extension and intension of concepts, and together they form a complete lattice. By Birkhoff's representation theorem, every complete lattice can be represented in this way. Consequently, the logic of formal concepts can be understood as the logic of lattices. This logic, along with its modal extensions and their connection to FCA, has been actively studied in recent years. However, to capture realistic forms of reasoning, it is essential to formalize defeasible reasoning on concepts.
In this talk, I present a generalization of KLM-style defeasible reasoning to the conceptual framework. Specifically, the framework introduces different notions of defeasible inclusion—forms of inclusion that typically hold by default but may be overridden by exceptions in the extension, intension, or both—by generalizing the cumulative reasoning system and the cumulative reasoning system with a loop to the conceptual setting. Furthermore, we extend cumulative models, cumulative ordered models, and preferential models to the conceptual domain and establish soundness and completeness results for these generalized models.