Representing and Processing Medical Knowledge Using Formal Concept Analysis

Summary

Objectives: The aim is to show the flexibility, adequateness, and generality of formal concept analysis (FCA) applied to expert systems in medicine.

Methods: The basic idea of formal concept analysis is to look at a set of objects together with their attributes (formal context) under a definite mathematical view. This view leads to a mathematical structure, a complete lattice, which can be represented graphically.

Results: Some examples show that this method is very general and can be used to describe diseases, relationships between diseases and findings, the inference process, and, among others, types of uncertainty. For many applications, the adequateness of this method, concerning the underlying semantics, can easily be made plausible.

Conclusions: FCA can be used to analyze data that can be described by objects and attributes of any kind. The selected examples (diseases, patient cases, therapeutic decisions, rules) show the usefulness of this method. Although it is not difficult to transform the relevant semantics into a formal context in many cases, much more experience is necessary.

Keywords

Knowledge representation - computer-assisted medical decision making - formal concept analysis - inference algorithms - expert systems

• References

• 1 Shortliffe EH. Computer-based medical consultations: MYCIN. New York: Elsevier; 1976
• 2 Minsky M. A framework for representing knowledge. In: The Psychology of Computer Vision. Winston PH. ed. New York: McGraw-Hill; 1975: 211-77.
• 3 Aikins JS. Prototypical Knowledge for Expert Systems. Artificial Intelligence 1983; 20: 163-210.
• 4 Woods WA. What’s in a link: Foundations for semantic networks. In: Representation and Understanding. Bobrow DG, Collins A. eds. New York: Academic Press; 1975: 35-82.
• 5 Sowa JF. ed. Principles of Semantic Networks. San Mateo, CA: Morgan Kaufmann; 1991
• 6 Feller W. An Introduction to Probability Theory and its Applications (2nd ed, vol I). New York: John Wiley; 1960
• 7 Zadeh LA. Fuzzy sets. Information and Control 1965; 8: 338-53.
• 8 Zadeh LA. The role of fuzzy logic in the management of uncertainty in expert systems. Fuzzy Sets and Systems 1983; 11: 199-227.
• 9 Adlassnig K-P. A fuzzy logical model of computer-assisted medical diagnosis. Methods Inf Med 1980; 19: 141-8.
• 10 Dempster AP. Upper and lower probabilities induced by a multivalued mapping. Annals of Mathematical Statistics 1967; 38: 325-39.
• 11 Shafer GA. Mathematical theory of evidence. Princeton, NJ: Princeton University Press; 1976
• 12 Cheeseman P. Probabilistc versus fuzzy reasoning. In: Uncertainty in Artificial Intelligence. Kanal LN, Lemmer JF. eds. Amsterdam: North-Holland; 1986: 85-102.
• 13 Zadeh LA. Is probability theory sufficient for dealing with uncertainty in AI:A negative view. In: Uncertainty in Artificial Intelligence. Kanal LN, Lemmer JF. eds. Amsterdam: North-Holland; 1986: 103-16.
• 14 Halpern JY, Fagin R. Two views of belief: Belief as generalized probability and belief as evidence. Artificial Intelligence 1992; 54: 275-317.
• 15 Miller RA. Internist-1/Caduceus: Problems facing expert consultant programs. Methods Inf Med 1984; 23: 9-14.
• 16 Reggia JA, Nau DS, Wang PY. Diagnostic expert systems based on a set covering model. Int J Man-Machine Studies 1983; 19: 437-60.
• 17 Reggia JA, Nau DS, Wang PY. A formal model of diagnostic inference. I. Problem formulation and decomposition. Information Sciences 1985; 37: 227-56.
• 18 Weiss SM, Kulikowski CA, Amarel S, Safir A. A model-based method for computer-aided medicial decision-making. Artificial Intelligence 1978; 11: 145-72.
• 19 Patil RS, Szolovits P, Schwartz WB. Causal understanding of patient illness in medical diagnosis. In: Readings in Medical Artificial Intelligence – The First Decade. Clancey WJ, Shortliffe EH. eds. Reading, MA: Addison-Wesley; 1984: 339-60.
• 20 Musen MA, Van der Lei J. Knowledge engineering for clinical consultation programs: Modeling the application area. Methods Inf Med 1989; 28: 28-35.
• 21 Ganter B, Wille R. Formal Concept Analysis – Mathematical Foundations. Berlin: Springer-Verlag; 1999
• 22 Schnabel M. Expertensysteme in der Medizin – Eine Einführung mit Beispielen. Stuttgart: Gustav Fischer Verlag; 1996
• 23 Birkhoff G. Lattice Theory (3rd ed). Providence, Rhode Island: American Mathematical Society; 1973
• 24 Thurmayr R, Thurmayr GR. Quality management using information systems. In: New Aspects of High Technology in Medicine. Bruch H-P, Köckerling F, Bouchard R, Schug-Pass C. eds. Bologna: Monduzzi Editore; 2000: 449-53.
• 25 Thurmayr GR, Thurmayr R. Automation of medical data management by knowledge-based systems. Artif Intell Med. 2002
• 26 Rector AL. Thesauri and formal classification: Terminologies for people and machines. Methods Inf Med 1998; 37: 501-9.
• 27 Graf PF, Klöppel M, Höhnke C, Kovacs L. Rekonstruktion der Greiffunktion durch Fingerersatz. Abteilung für Plastische- & Wiederherstellungs-Chirurgie, Klinikum rechts der Isar, Technische Universität München. Available at: http://www.plastchir.med.tu-muenchen.de/texte/fingerersatz/fingerersatz.htm.
• 28 Pople Jr HE. Heuristic methods for imposing structure on ill-structured problems: The structuring of medical diagnostics. In: Artificial Intelligence in Medicine. Szolovits P. Boulder, CO: Westview Press; 1982: 119-90.
• 29 Dojat M, Pachet F. Effective Domain-dependent reuse in Medical Knowledge Bases. Comput Biomed Res 1995; 28: 403-32.
• 30 Smart JF, Roux M. A model for medical knowledge representation application to the analysis of descriptive pathology reports. Methods Inf Med 1995; 34: 352-60.
• 31 Kolles H, Remberger K. How to build a computer-assisted, diagnosis-finding system – An example in dermatopathology. Arch Pathol Lab Med 1991; 115: 1011-5.
• 32 Hayes-Roth B, Washington R, Ash D, Hewett R, Collinot A, Vina A, Seiver A. Guardian: A prototype intelligent agent for intensive-care monitoring. Artif Intell Med 1992; 4: 165-85.
• 33 López B, Plaza E. Case-based planning for medical diagnosis. In: Methodologies for Intelligent Systems. Komorowski J, Raś ZW. eds. Berlin: Springer-Verlag; 1993: 96-105.
• 34 Console L, Theseider Dupré D, Torasso P. A theory of diagnosis for incomplete causal models. In: Proc. 11^th Internat. Joint Conference on Artificial Intelligence. Sridharan NS. ed. San Mateo, CA: Morgan Kaufmann; 1989: 1311-7.
• 35 Van Ginneken AM. Commentary “Diagnostic support: Towards the intelligent integrated reference source”. In: Yearbook of Medical Informatics ’99. Van Bemmel JH, McCray AT. Stuttgart-New York: Schattauer Verlag; 1999: 175-9.
• 36 Chandrasekaran B, Tanner MC. Uncertainty handling in expert systems: Uniform vs. task-specific formalisms. In: Uncertainty in Artificial Intelligence. Kanal LN, Lemmer JF. eds. Amsterdam: North-Holland; 1986: 35-46.
• 37 Scheich P, Skorsky M, Vogt F, Wachter C, Wille R. Conceptual data systems. In: Information and Classification – Concepts, Methods and Applications. Opitz O, Lausen B, Klar R. eds. Berlin: Springer-Verlag; 1993: 72-84.
• 38 Pauker SG, Gorry GA, Kassirer JP, Schwartz WB. Towards the simulation of clinical cognition – Taking a present illness by computer. Am J Med 1976; 60: 981-96.
• 39 Warner Jr HR. Iliad: Moving medical decision-making into new frontiers. Methods Inf Med 1989; 28: 370-2.
• 40 Lau LM, Warner HR. Performance of a diagnostic system (Iliad) as a tool for quality assurance. Comput Biomed Res 1992; 25: 314-23.
• 41 Burmeister P, Holzer R. On the treatment of incomplete knowledge in formal concept analysis. In: Conceptual Structures: Logical, Linguistic, and Computational Issues. Ganter B, Mineau GW. eds. Berlin: Springer-Verlag; 2000: 385-98.
• 42 Gorry GA, Silverman MS, Pauker SG. Capturing clinical expertise – A computer program that considers clinical responses to digitalis. Am J Med 1978; 64: 452-60.
• 43 Davis R. Interactive transfer of expertise: Acquisition of new inference rules. Artificial Intelligence 1979; 12: 121-57.
• 44 Kassirer JP, Kuipers BJ, Gorry GA. Toward a theory of clinical expertise. Am J Med 1982; 73: 251-9.
• 45 Weiss SM, Kulikowski CA. A Practical Guide to Designing Expert Systems. London: Chapman and Hall; 1984
• 46 Van Bemmel JH. Criteria for the acceptance of decision-support systems by clinicians; lessons from ECG interpretation systems. In: Artificial Intelligence in Medicine. Andreassen S, Engelbrecht R, Wyatt J. eds. Amsterdam: IOS Press; 1993: 7-10.
• 47 Van Bemmel JH. Medical informatics, art or science?. Methods Inf Med 1996; 35: 157-72.
• 48 Lenz M, Burkhard H-D, Pirk P, Auriol E, Manago M. CBR for diagnosis and decision support. Ai Communications 1996; 9: 138-46.
• 49 Connelly DP, Johnson PE. The medical problem solving process. Hum Pathol 1980; 11: 412-9.
• 50 Degoulet P, Fieschi M, Chatellier G. Decision support systems from the standpoint of knowledge representation. Methods Inf Med 1995; 34: 202-8.
• 51 Aamodt A, Plaza E. Case-based reasoning: Foundational issues, methodological variations, and system approaches. Ai Communications 1994; 7: 39-59.
• 52 Miller RA, Pople Jr HE, Myers JD. Internist-1 – An experimental computer-based diagnostic consultant for general internal medicine. N Engl J Med 1982; 307: 468-76.
• 53 Aliferis CF, Miller RA. On the heuristic nature of medical decision-support systems. Methods Inf Med 1995; 34: 5-14.
• 54 Buchanan BG, Barstow D, Bechtal R, Bennett J, Clancey W, Kulikowski C, Mitchell T, Waterman DA. Constructing an expert system. In: Building Expert Systems. Hayes-Roth F, Waterman DA, Lenat DB. eds. Reading, MA: Addison-Wesley; 1983: 127-67.
• 55 Musen MA. Automated Generation of Model-based Knowledge Acquisition Tools. London: Pitman; 1989
• 56 Alpar P. Toward structured expert systems development. Expert Systems with Applications 1990; 1: 63-70.
• 57 Newell A. The knowledge level. Artificial Intelligence 1982; 18: 87-127.
• 58 Gierl L, Bull M, Schmidt R. CBR in medicine. In: Case-Based Reasoning Technology. Lenz M, Bartsch-Spörl B. eds. Berlin: Springer-Verlag; 1998: 273-97.