Proof of the basic theorem on concept lattices in Isabelle/HOL

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Thesis Type: Postgraduate

Institution Of The Thesis: Middle East Technical University, Turkey

Approval Date: 2003

Thesis Language: English

Student: Barış Sertkaya

Co-Supervisor: MEHMET HALİT S. OĞUZTÜZÜN, Mehmet Oğuztüzün

Abstract:

Formel Concept Analysis is an emerging field of applied mathematics based on a lattice-theoretic formalization of the notions of concept and conceptual hierarchy. It thereby facilitates mathematical thinking for conceptual data analysis and knowledge processing. Isabelle, on the other hand, is a generic interactive theory development environment for implementing logical formalisms. It has been instantiated to support reasoning in several object-logics. Specialization of Isabelle for Higher Order Logic is called Isabelle/HOL. Our long term is to formalize the theory of Formal Concept Analysis in Isabelle/HOL. This will provide a mechanized theory for researchers who want to prove their own theorems with utmost precision, and for developers who want to design knowledge processing algorithms. The speccific accomplishment of this thesis is a machinechecked version of the proof of the Basic Theorem of Concept Lattices, which appears in the book "Formal Concept Analysisé by Ganter and Wille. As a by product, the underlying lattice theory by F. Kammueller has been extended.