Conceptual Knowledge Processing with Formal Concept Analysis and Ontologies

Cimiano P, Stumme G, Hotho A, Tane J. Conceptual Knowledge Processing with Formal Concept Analysis and Ontologies. In: Eklund PW, ed. Concept Lattices, Second International Conference on Formal Concept Analysis, ICFCA 2004, Sydney, Australia, February 23-26, 2004, Proceedings. Lecture Notes in Computer Science, 2961. Springer; 2004: 189-207

On the isomorphism problem of concept algebras

Weakly dicomplemented lattices are bounded lattices equipped with two unary operations to encode a negation on {\it concepts}. They have been introduced to capture the equational theory of concept algebras \cite{Wi00}. They generalize Boolean algebras. Concept algebras are concept lattices, thus complete lattices, with a weak negation and a weak opposition. A special case of the representation problem for weakly dicomplemented lattices, posed in \cite{Kw04}, is whether complete {\wdl}s are isomorphic to concept algebras. In this contribution we give a negative answer to this question (Theorem \ref{T:main}). We also provide a new proof of a well known result due to M.H. Stone \cite{St36}, saying that {\em each Boolean algebra is a field of sets} (Corollary \ref{C:Stone}). Before these, we prove that the boundedness condition on the initial definition of {\wdl}s (Definition \ref{D:wdl}) is superfluous (Theorem \ref{T:wcl}, see also \cite{Kw09}).Comment: 15 page

On the isomorphism problem of concept algebras

Weakly dicomplemented lattices are bounded lattices equipped with two unary operations to encode a negation on concepts. They have been introduced to capture the equational theory of concept algebras (Wille 2000; Kwuida 2004). They generalize Boolean algebras. Concept algebras are concept lattices, thus complete lattices, with a weak negation and a weak opposition. A special case of the representation problem for weakly dicomplemented lattices, posed in Kwuida (2004), is whether complete weakly dicomplemented lattices are isomorphic to concept algebras. In this contribution we give a negative answer to this question (Theorem4). We also provide a new proof of a well known result due to M.H. Stone(Trans Am Math Soc 40:37-111, 1936), saying that each Boolean algebra is a field of sets (Corollary4). Before these, we prove that the boundedness condition on the initial definition of weakly dicomplemented lattices (Definition1) is superfluous (Theorem1, see also Kwuida (2009)

Querying a Bioinformatic Data Sources Registry with Concept Lattices

ISSN 0302-9743 (Print) 1611-3349 (Online) ISBN 978-3-540-27783-5International audienceBioinformatic data sources available on the web are multiple and heterogenous. The lack of documentation and the difficulty of interaction with these data banks require users competence in both informatics and biological fields for an optimal use of sources contents that remain rather under exploited. In this paper we present an approach based on formal concept analysis to classify and search relevant bioinformatic data sources for a given user query. It consists in building the concept lattice from the binary relation between bioinformatic data sources and their associated metadata. The concept built from a given user query is then merged into the concept lattice. The result is given by the extraction of the set of sources belonging to the extents of the query concept subsumers in the resulting concept lattice. The sources ranking is given by the concept specificity order in the concept lattice. An improvement of the approach consists in automatic refinement of the query thanks to domain ontologies. Two forms of refinement are possible by generalisation and by specialisation

Proceedings of the 5th International Workshop "What can FCA do for Artificial Intelligence?", FCA4AI 2016(co-located with ECAI 2016, The Hague, Netherlands, August 30th 2016)

International audienceThese are the proceedings of the fifth edition of the FCA4AI workshop (http://www.fca4ai.hse.ru/). Formal Concept Analysis (FCA) is a mathematically well-founded theory aimed at data analysis and classification that can be used for many purposes, especially for Artificial Intelligence (AI) needs. The objective of the FCA4AI workshop is to investigate two main main issues: how can FCA support various AI activities (knowledge discovery, knowledge representation and reasoning, learning, data mining, NLP, information retrieval), and how can FCA be extended in order to help AI researchers to solve new and complex problems in their domain. Accordingly, topics of interest are related to the following: (i) Extensions of FCA for AI: pattern structures, projections, abstractions. (ii) Knowledge discovery based on FCA: classification, data mining, pattern mining, functional dependencies, biclustering, stability, visualization. (iii) Knowledge processing based on concept lattices: modeling, representation, reasoning. (iv) Application domains: natural language processing, information retrieval, recommendation, mining of web of data and of social networks, etc