Defeasible Reasoning on Concepts
Yiwen Ding, Krishna Manoorkar, Ni Wayan Switrayni, Ruoding Wang
TL;DR
The paper extends KLM-style nonmonotonic reasoning toFormal Concept Analysis by developing conceptual versions of cumulative reasoning ($ extbf{CC}$), looped reasoning ($ extbf{CCL}$), and their semantic models. It replaces classical implication with lattice-compatible sequents and anchors semantics in pointed polarity-based models and concept lattices, proving soundness and completeness with respect to conceptual cumulative, ordered, and preferential models. An explicit canonical construction links defeasible relations to semantic models, and a representative example demonstrates nonmonotonic behavior and the failure of certain classical rules in the conceptual setting. The work lays foundations for defeasible concept reasoning and points to future work on rational monotonicity, ranked preference, and belief revision within FCA.
Abstract
In this paper, we take first steps toward developing defeasible reasoning on concepts in KLM framework. We define generalizations of cumulative reasoning system C and cumulative reasoning system with loop CL to conceptual setting. We also generalize cumulative models, cumulative ordered models, and preferential models to conceptual setting and show the soundness and completeness results for these models.