Preferential concept analysis: Extensions to formal concept analysis based on preferential reasoning
| dc.contributor.advisor | Meyer, Thomas | |
| dc.contributor.author | Carr, Lucas | |
| dc.date.accessioned | 2026-11-12T13:36:43Z | |
| dc.date.available | 2026-11-12T13:36:43Z | |
| dc.date.issued | 2026 | |
| dc.date.updated | 2026-11-12T13:33:46Z | |
| dc.description.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. | |
| dc.identifier.apacitation | Carr, L. (2026). <i>Preferential concept analysis: Extensions to formal concept analysis based on preferential reasoning</i>. (). University of Cape Town ,Faculty of Science ,Department of Computer Science. Retrieved from http://hdl.handle.net/11427/43939 | en_ZA |
| dc.identifier.chicagocitation | Carr, Lucas. <i>"Preferential concept analysis: Extensions to formal concept analysis based on preferential reasoning."</i> ., University of Cape Town ,Faculty of Science ,Department of Computer Science, 2026. http://hdl.handle.net/11427/43939 | en_ZA |
| dc.identifier.citation | Carr, L. 2026. Preferential concept analysis: Extensions to formal concept analysis based on preferential reasoning. . University of Cape Town ,Faculty of Science ,Department of Computer Science. http://hdl.handle.net/11427/43939 | en_ZA |
| dc.identifier.ris | TY - Thesis / Dissertation AU - Carr, Lucas AB - 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. DA - 2026 DB - OpenUCT DP - University of Cape Town KW - Formal Concept Analysis (FCA) LK - https://open.uct.ac.za PB - University of Cape Town PY - 2026 T1 - Preferential concept analysis: Extensions to formal concept analysis based on preferential reasoning TI - Preferential concept analysis: Extensions to formal concept analysis based on preferential reasoning UR - http://hdl.handle.net/11427/43939 ER - | en_ZA |
| dc.identifier.uri | http://hdl.handle.net/11427/43939 | |
| dc.identifier.vancouvercitation | Carr L. Preferential concept analysis: Extensions to formal concept analysis based on preferential reasoning. []. University of Cape Town ,Faculty of Science ,Department of Computer Science, 2026 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/43939 | en_ZA |
| dc.language.iso | en | |
| dc.language.rfc3066 | eng | |
| dc.publisher.department | Department of Computer Science | |
| dc.publisher.faculty | Faculty of Science | |
| dc.publisher.institution | University of Cape Town | |
| dc.subject | Formal Concept Analysis (FCA) | |
| dc.title | Preferential concept analysis: Extensions to formal concept analysis based on preferential reasoning | |
| dc.type | Thesis / Dissertation | |
| dc.type.qualificationlevel | Masters | |
| dc.type.qualificationlevel | MSc |