From Concept Lattice to Approximation Space: Algebraic Structure of Some Spaces of Partial Objects¹

Article type: Research Article

Authors: Pagliani, Piero

Affiliations: Research Group on Learning and Communication Models, Education Centre, ITALSIEL-FINSIEL, La Rustica, Via F. Depero 24, 00155 Roma, Italy

Note: [1] This study has been supported by the Production Laboratory of the Education Centre of ITALSIEL within the reserarches on student knowledge modelling.

Abstract: The paper presents general logic-algebraic structures related to Wille’s Concept Lattices, Pawlak’s theory of Information Systems and Approximation Spaces. These structures are studied in order to analyse increasing concepts definitions and decreasing objects identifications. Here they are investigated starting from the notions of polarity and quantum at a point, applying the approach used in Bell’s representation theorem for ortholattices and the mathematical tools provided by pointless topology. In this way we intend to connect this analysis to the notion of topology of positive information introduced in Scott’s Information Systems and Scott’s Domains. In particular, notions connected to the concept of ‘objects definition improvement’ (via attributes, or parameters) are algebraically investigated in order to analyse general and particular characteristics of Information Systems and a related classification for them is proposed.

DOI: 10.3233/FI-1993-18102

Journal: Fundamenta Informaticae, vol. 18, no. 1, pp. 1-25, 1993