Preferential concept analysis: Extensions to formal concept analysis based on preferential reasoning

Carr, Lucas

Preferential concept analysis: Extensions to formal concept analysis based on preferential reasoning

Thesis / Dissertation

2026

Publisher

University of Cape Town

Department

Department of Computer Science

Faculty

Faculty of Science

Abstract

Formal Concept Analysis (FCA) is a mathematical framework for representing and reasoning about data. Central to FCA is the construction of formal concepts, each consisting of a set of objects—the extension—and a set of attributes—the intension. These concepts are ordered by a natural sub-super concept relation, forming a lattice known as the concept lattice. A second key aspect of FCA is the discovery of attribute implications, which are statements of the form 𝑋 → 𝑌, expressing that all objects possessing the attributes 𝑋 necessarily possess the attributes 𝑌. However, attribute implications are strict, and cannot tolerate the existence of exceptions. In real-world data, such dependencies between attributes rarely hold universally, and instead tend to hold typically, admitting occasional counterexamples. The KLM framework, introduced by Kraus, Lehmann, and Magidor, provides an approach to defeasible reasoning in propositional logic, supporting the expression of defeasible conditional statements such as ‘typically, 𝑋 → 𝑌’. In this dissertation, we investigate how the ideas from the KLM framework may be reconstituted into the setting of FCA. We show that their faithful translation is indeed possible, and explore the questions that emerge from this new setting in particular, how defeasible reasoning within a context differs from its propositional counterpart. We also contribute a defeasible basis, which compresses the defeasible information of a context into a minimal, non-redundant set of rules from which all other defeasible rules may be derived. Finally, we explore how the introduction of defeasible reasoning gives rise to a notion of prototypicality for concepts in FCA. We define rational concepts as an initial formalisation of this prototypicality, and discuss how the definition leads to a breakdown of the natural conceptual hierarchy.

Keywords

Formal Concept Analysis (FCA)

Reference:

Collections

Masters

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