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Formal Context Analysis in Rapidly Evolving Knowledge Webs



On-the-fly personalised assembly of complex objects (learning materials, contracts, plans, designs, systems and network configurations, etc) is increasingly expected in knowledge processing and decision making. This requires the discovery of discrete underlying models and taxonomies of subject domains and statistical matching in dynamically varying contexts defined by changing personal preferences, tasks, objectives and other characteristics. This project addresses formal models of context, context exploration and similarity based in applied lattice theory, its connection to algebra and logic, and combined with statistical retrieval. Parallel algorithms will be developed, analysed and benchmarked to enable high-performance processing of vast numbers of heterogeneous objects and their dynamic configuration in rapidly varying contexts.


context-aware computing; decision-support systems; formal concept analysis; formal logic; lattice theory; evolving knowledge webs; information systems; parallel algorithms.



The project aims to develop a model for context termed Formal Context Analysis. This model will be based on the notion of context as formalised in Formal Concept Analysis (FCA) [GaW1997] -- a branch of applied lattice theory. In FCA contexts are collections of objects, given a priori, with a fixed static characterisation of attributes. Our extension will make contexts first-class objects, will allow objects to be characterised in multiple incomplete contexts simultaenously, and in rapidly changing contexts. Statistical similarity of contexts will be modelled to cater for handling of very large numbers of objects in large numbers of overlapping contexts and for dealing with context independently of meta data. Relevant FCA algorithms, for matching contexts and discovering structure in unstructured domains, will be extended accordingly and parallel methods will be studied and realised to enable high-performance context manipulation and transformations. These will be trialed in an industry collaboration in an existing system which already separates content and context management in its core decision support engine. Case studies will be conducted in domains such as adaptive e-learning, ad-hoc networks and self-configuring distributed systems.

Figure 1.

Impression: Bauhaus Crystal Galois connection (hws)


Industry, government and educational institutions of our emerging knowledge economy are increasingly interconnected in webs of knowledge resources (knowledge objects) and knowledge processing services (service components). The distributed sources of knowledge, from which documents are constructed on-the-fly, and the distributed components which are sourced to provide coordinated services, have evolved around different conceptual models, taxonomies and domain-specific languages. Organising knowledge objects dynamically for the knowledge worker requires automatic discovery of such underlying models and taxonomies. Organising and configuring service components is increasingly required under dynamically changing constraints for quality and cost of service. Context processing is then becoming a key to honing knowledge spaces and services under given organizational objectives, current tasks in a workflow, user goals or system objective functions, historic profiles and other contextual characteristics.

The formalisation of context proposed here will necessarily include rapid dynamic change and adaptability. Examples of practical relevance of such concepts and references to prior work include:

Context handling and its relation to contents classified and structured on-the fly has received little attention in research but is currently of increasing interest in several other domains too. For example in pervasive computing software on small devices must increasingly adapt to rapidly changing contexts dominantly defined by location. In virtual reality systems relations between objects change dynamically and rapidly. A fundamental approach to context based in formal theories of information, structure and reasoning is therefore highly desirable and has a chance of wide applicability.

Monash University
Prof H. Schmidt Chief Investigator (Project Leader)
Dr D. Squire Chief Investigator  
Ian Thomas Research Fellow (Project Manager)
Jane Jayaputera Research Assistant (part-time)
Terence Law Research Assistant (part-time)
PhD Student
Sponsors (7/2004-6/2007)
Australian Research Council ARC Linkage LP0455105
Opaltree Systems Pty/Ltd Industry Partner


[GaW1997] Ganter, B. and Wille, R. (1997)Applied lattice theory: Formal concept analysis, On-line preprint:

[Kraemer01] Kraemer and H. Schmidt: Components and Tools for Online Education. European Journal of Education, vol. 36, no. 2, 2001

[Schmidt04] H W Schmidt, B J Krämer, I Poernomo and R Reussner: ``Predictable Component Architectures Using Dependent Finite State Machines'', LNCS 2941, (Proceedings of the 9th International Workshop in Radical Innovations of Software and Systems Engineering in the Future, Venice, Italy), Springer-Verlag, pp. 310-324

[Schmidt02] Heinz W. Schmidt, Ralf H. Reussner. Generating Adapters for Concurrent Component Protocol Synchronisation Proceedings of the Fifth IFIP International conference on Formal Methods for Open Object-based Distributed Systems, Kluwer, March, 4/2002

[Wegner00] Wegner, L. and Schmidt, H. W.: \newblock Shared XML documents in service centres of the future, IEEE Proc. 10th Intl Database Symposium (IDS2000), IEEE, 2000.

[Zeller97] Zeller, A. and Snelting, G (1997) Unified versioning through feature logic, ACM Transactions on Software Engineering and Methodology 6(4), pp. 398--441.


[ICFCA 2004] International Conference on Formal Concept Analysis, LNCS 2961, Springer, Feb 2004

[FCAWeb] Formal Concept Analysis Web

[Tam03] Gordon Tam's BSE 4th year project 2003

Web content: Heinz W. Schmidt and David Squire; Graphics: Heinz W. Schmidt.
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