Combinatorics: set systems, hypergraphs, families of vectors, and combinatorial probability
Combinatorics: set systems, hypergraphs, families of vectors, and combinatorial probability
A modal logic for subjective default reasoning
Artificial Intelligence
Formal Concept Analysis: Mathematical Foundations
Formal Concept Analysis: Mathematical Foundations
Structural Machine Learning with Galois Lattice and Graphs
ICML '98 Proceedings of the Fifteenth International Conference on Machine Learning
Generalized Formal Concept Analysis
ICCS '00 Proceedings of the Linguistic on Conceptual Structures: Logical Linguistic, and Computational Issues
Pattern Structures and Their Projections
ICCS '01 Proceedings of the 9th International Conference on Conceptual Structures: Broadening the Base
Discrete Applied Mathematics - Special issue: The 1998 conference on ordinal and symbolic data analysis (OSDA '98)
Maximal and stochastic Galois lattices
Discrete Applied Mathematics - Special issue: The 1998 conference on ordinal and symbolic data analysis (OSDA '98)
Introduction to logical information systems
Information Processing and Management: an International Journal
Generating a Condensed Representation for Association Rules
Journal of Intelligent Information Systems
Lattices with Interior and Closure Operators and Abstract Approximation Spaces
Transactions on Rough Sets X
The equivalence of model-theoretic and structural subsumption in description logics
IJCAI'93 Proceedings of the 13th international joint conference on Artifical intelligence - Volume 1
Incremental construction of alpha lattices and association rules
KES'10 Proceedings of the 14th international conference on Knowledge-based and intelligent information and engineering systems: Part II
Alpha galois lattices: an overview
ICFCA'05 Proceedings of the Third international conference on Formal Concept Analysis
Negation, opposition, and possibility in logical concept analysis
ICFCA'06 Proceedings of the 4th international conference on Formal Concept Analysis
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We present a view of abstraction based on a structure preserving reduction of the Galois connection between a language L of terms and the powerset of a set of instances O. Such a relation is materialized as an extension-intension lattice, namely a concept lattice when L is the powerset of a set P of attributes. We define and characterize an abstraction A as some part of either the language or the powerset of O, defined in such a way that the extension-intension latticial structure is preserved. Such a structure is denoted for short as an abstract lattice. We discuss the extensional abstract lattices obtained by so reducing the powerset of O, together together with the corresponding abstract implications, and discuss alpha lattices as particular abstract lattices. Finally we give formal framework allowing to define a generalized abstract lattice whose language is made of terms mixing abstract and non abstract conjunctions of properties.