Skip to main content
SpringerLink
Log in

Consistent structuring of inconsistent knowledge

  • Published:
Journal of Intelligent Information Systems Aims and scope Submit manuscript

Abstract

Inconsistency handling is one of the central problems in many areas of AI. There are different approaches to dealing with contradictions and other types of inconsistency. In this paper, we develop an approach based on logical varieties and prevarieties, which are complex structures constructed from logical calculi. Being locally isomorphic to a logical calculus, globally logical varieties form a logical structure, which allows representation of inconsistent knowledge in a consistent way and provides much more flexibility and efficacy for AI than standard logical methods. Problems of logical variety immersion into a logical calculus are studied. Such immersions extend the local structure of a logical calculus to the global structure of a logical variety. The obtained results demonstrate when it is possible to use standard logical tools, such as logical calculi, and when it is necessary to go beyond this traditional technique. Finally a particular logical variety, the Logic of Reasonable Inferences, applied to the design of legal knowledge based systems is described.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Abadi, A., Rabinovich, A., Sagiv, M. (2010). Decidable fragments of many-sorted logic. Journal of Symbolic Computation, 45(2), 153–172.

    Article  MathSciNet  Google Scholar 

  • Ackermann, W. (1940). Zur Widerspruchsfreiheit der Zahlentheorie. Annals of Mathematics, 117, 162–194.

    Article  MathSciNet  Google Scholar 

  • Amgoud, L., & Cayrol, C. (1998). On the acceptability of arguments in preference-based argumentation. In Proceedings of 14th conference on uncertainty in artificial intelligence (UAI’98) (pp. 1–7).

  • Amir, E. (2002). Dividing and conquering logic. PhD thesis, Computer Science Department, Stanford University.

  • Amir, E., & McIlraith, S. (2005). Partition-based logical reasoning for first-order and propositional theories. Artificial Intelligence, 162(1–2), 49–88.

    Article  MathSciNet  Google Scholar 

  • Balzer, R. (1991). Tolerating inconsistency. In Proceedings of 13th international conference on software engineering (ICSE-13), Austin, TX, USA (pp. 158–165). Silver Spring, MD: IEEE Computer Society Press.

    Google Scholar 

  • Barwise, J., & Seligman, J. (1997). Information flow: The logic of distributed systems. Cambridge tracts in theoretical computer science 44. Cambridge: Cambridge University Press.

    Book  Google Scholar 

  • Benferhat, S., & Garcia, L. (2002). Handling locally stratified inconsistent knowledge bases. Studia Logica, 70, 77–104.

    Article  MathSciNet  Google Scholar 

  • Benferhat, S., Cayrol, C., Dubois, D., Lang, J., Prade, H. (1993). Inconsistency management and prioritized syntax-based entailment. In Proceedings of 13th international joint conference on artificial intelligence (IJCAI‘93) (pp. 640–645).

  • Benferhat, S., Dubois, D., Prade, H. (1992). Representing default rules in possibilistic logic. In Proceedings of 3rd international conference of principles of knowledge representation and reasoning (KR‘92) (pp. 673–684).

  • Benferhat, S., Dubois, D., Prade, H. (1995). How to infer from inconsistent beliefs without revising? In Proc. of 14th int. joint conf. on artif. intelligence (IJCAI‘95).

  • Bertossi, L.E., Hunter, A., Schaub, T. (Eds.) (2005). Inconsistency tolerance. LNCS (Vol. 3300). Heidelberg: Springer.

    Google Scholar 

  • Besnard, P., & Hunter, A. (1995). Quasi-classical logic: Non-trivializable classical reasoning from inconsistent information. In Proc. of ECSQARU‘95. LNAI (Vol. 946, pp. 44–51).

  • Binas, A., & McIlraith, S. (2008). Peer-to-peer query answering with inconsistent knowledge. In Proceedings on the 11th international conference on principles of knowledge representation and reasoning, Sydney, Australia (pp. 329–339).

  • Brewka, G. (1989). Preferred subtheories: An extended logical framework for default reason. In Proceedings of 11th international joint conference on artificial intelligence (IJ CAI‘89) (pp. 1043–1048).

  • Brown, B., & Priest, G. (2004). Chunk and permeate: a paraconsistent inference strategy, part I: The infinitesimal calculus. Journal of Philosophy Logic, 33(4), 379–388.

    Article  MathSciNet  Google Scholar 

  • Burgin, M. (1991). Logical methods in artificial intelligent systems. Vestnik of the Computer Society, 2, 66–78 (in Russian).

    Google Scholar 

  • Burgin, M. (1997). Logical varieties and covarieties. Methodological and theoretical problems of mathematics and information and computer sciences, Kiev (pp. 18–34) (in Russian).

  • Burgin, M. (2004). Logical tools for program integration and interoperability. In Proceedings of the IASTED international conference on software engineering and applications (pp. 743–748). Cambridge: MIT.

    Google Scholar 

  • Burgin, M., & de Vey Mestdagh, C.N.J. (2011). The representation of inconsistent knowledge in advanced knowledge based systems. Lecture notes in computer science. Knowlege-Based and Intelligent Information and Engineering Systems, 6882, 524–537.

    Article  Google Scholar 

  • Cuzzocrea, A. (2004). Knowledge on the web: Making web services knowledge-aware. In Proceedings. IEEE/WIC/ACM international conference on web intelligence, WI 2004 (pp. 419–426).

  • Cuzzocrea, A. (2006). Combining multidimensional user models and knowledge representation and management techniques for making web services knowledge-aware. Web Intelligence and Agent Systems, 4(3), 289–312.

    Google Scholar 

  • Cuzzocrea, A., & Mastroianni, C.A. (2003). Reference architecture for knowledge management-based web systems. In WISE 2003 (pp. 347–354).

  • Da Costa, N.C.A. (1963). Calcul propositionnel pour les systemes formels inconsistants. Compte Rendu Academie des Sciences (Paris), 257, 3790–3792.

    Google Scholar 

  • Dalal, M. (1988). Investigations into a theory of knowledge base revision: Preliminary report. In Proceedings of the seventh national conference on artificial intelligence (AAAI’88) (pp. 475–479).

  • Delgrande, J.P., & Mylopoulos, J. (1986). Knowledge representation: Features of knowledge. In Fundamentals of artificial intelligence (pp. 3–38). Berlin, New York, Tokyo: Springer Verlag.

    Google Scholar 

  • de Vey Mestdagh, C.N.J. (1998). Legal expert systems. Experts or expedients? The representation of legal knowledge in an expert system for environmental permit law. In C. Ciampi & E. Marinai (Eds.), The law in the information society, conference proceedings on CD-Rom (p. 8). Firenze.

  • de Vey Mestdagh, C.N.J., & Hoepman, J.H. (2011). Inconsistent knowledge as a natural phenomenon: The ranking of reasonable inferences as a computational approach to naturally inconsistent (Legal) theories. In G. Dodig-Crnkovic & M. Burgin (Eds.), Information and computation. Essays on the scientific and philosophical understanding of the foundations of information and computation (pp. 439–476). New Jersey: World Scientific Publishing Co.

    Chapter  Google Scholar 

  • de Vey Mestdagh, C.N.J., Verwaard, W., Hoepman, J.H. (1991). The logic of reasonable inferences. In J.A. Breuker, R.V. de Mulder, J.C. Hage (Eds.), Legal knowledge based systems, model-based legal reasoning. Proc. 4th annual JURIX conference on legal knowledge based systems (pp. 60–76). Lelystad: Vermande.

    Google Scholar 

  • DeWitt, B.S. (1971). The many-universes interpretation of quantum mechanics. In Foundations of quantum mechanics (pp. 167–218). New York: Academic Press.

    Google Scholar 

  • Dung, P.M. (1995). On the acceptability of arguments and its fundamental role in non-monotonic reasoning, logic programming and n-person games. Artificial Intelligence, 77, 321–357.

    Article  MathSciNet  Google Scholar 

  • Dylla, M., Sozio, M., Theobald, M. (2011). Resolving temporal conflicts in inconsistent RDF knowledge bases. In BTW 2011 (pp. 474–493).

  • Easterbrook, S.M. (1996). Learning from inconsistency. In Proceedings of 8th international workshop on software specification and design (IWSSD-8), Paderborn, Germany, 22–23 March 1996 (pp. 136–140). Silver Spring, MD: IEEE Computer Society Press.

    Google Scholar 

  • Everett, H. (1957). Relative state formulation of quantum mechanics. Reviews of Modern Physics, 29, 454–462.

    Article  MathSciNet  Google Scholar 

  • Friedman, N., & Halpern, J.Y. (1994). A knowledge-based framework for belief change, part II: Revision and update. In Proceedings of the fourth international conference on the principles of knowledge representation and reasoning (KR’94) (pp. 190–200).

  • Gabbay, D. (1999). Fibring logics. Oxford: Clarendon Press.

    Google Scholar 

  • Gabbay, D., & Hunter, A. (1991). Making inconsistency respectable: A logical framework for inconsistency in reasoning, part 1 – a position paper. In Proceedings of fundamentals of artificial intelligence research’91 (pp. 19–32). Berlin: Springer.

    Chapter  Google Scholar 

  • Gabbay, D., & Hunter, A. (1992). Making inconsistency respectable: A logical framework for inconsistency in reasoning, part 2. In Symbolic and quantitative approaches to reasoning and uncertainty. Lecture notes in computer science (pp. 129–136). Springer, Berlin.

    Google Scholar 

  • Gärdenfors, P. (1988). Knowledge in flux - modeling the dynamic of epistemic states. Boston, MA: MIT Press.

    Google Scholar 

  • Gärdenfors, P., & Rott, H. (1995). Belief revision. In Handbook of logic in artificial intelligence and logic programming (Vol. 4, pp. 35–132). Oxford: Oxford University Press.

    Google Scholar 

  • Gentzen, G. (1936). Die Widerspruchfreiheit der reinen Zahlentheorie. Mathematische Annalen, 112, 493–565.

    Article  MathSciNet  Google Scholar 

  • Gödel, K. (1931–1932). Monatshefte für Mathematik und Physik. Akademische Verlags-Gesellschaft, Wien, Leipzig. Monatsh. Math. Phys., 38(1), 173–198.

    Google Scholar 

  • Hall, M. Jr. (1959). The theory of groups. New York: The Macmillan Company.

    Google Scholar 

  • Jaśkowski, S. (1948). Rachunek zdań dla systemów dedukcyjnych sprzecznych. Studia Societatis Scientiarun Torunesis (Sectio A), 1(5), 55–77.

    Google Scholar 

  • Lehmann, D. (1995a). Another perspective on default reasoning. Annals of Mathematics and Artificial Intelligence, 15, 61–82.

    Article  MathSciNet  Google Scholar 

  • Lehmann, D. (1995b). Belief revision, revised. In Proceedings of the fourteenth international joint conference on artificial intelligence (IJCAI’95) (pp. 1534–1540).

  • MacCartney, B., McIlraith, S.A., Amir, A., Uribe, T. (2003). Practical partition-based theorem proving for large knowledge bases. In Proceedings of the eighteenth international joint conference on artificial intelligence (IJCAI-03) (pp. 89–96).

  • Makinson, D. (2005). Bridges from classical to nonmonotonic logic. College Publications.

  • Marek, W., & Truszczynski, M. (1993). Nonmonotonic logics: Context-dependent reasoning. New York: Springer Verlag.

    Book  Google Scholar 

  • McDermott, D., & Doyle, J. (1980). Non-monotonic logic, I. Artificial Intelligence, 25, 41–72.

    Article  MathSciNet  Google Scholar 

  • McIlraith, S, & Amir, E. (2001). Theorem proving with structured theories. In Proceedings of the 17th intl’ joint conference on artificial intelligence (IJCAI ‘01) (pp. 624–631).

  • Meinke, K., & Tucker, J.V. (Eds.) (1993). Many-sorted logic and its applications. New York: John Wiley & Sons.

    Google Scholar 

  • Minsky, M. (1974). A framework for representing knowledge. Cambridge: MIT.

    Google Scholar 

  • Minsky, M. (1991a). Society of mind: a response to four reviews. Artificial Intelligence, 48, 371–396.

    Article  Google Scholar 

  • Minsky, M. (1991b). Conscious machines. In Machinery of consciousness, 75th anniversary symposium on science in society. National Research Council of Canada.

  • Nebel, B. (1991). Belief revision and default reasoning: syntax-based approaches. In Proceedings of the second international conference on the principles of knowledge representation and reasoning (KR‘91) (pp. 417–428).

  • Nebel, B. (1994). Base revision operations and schemes: semantics, representation and complexity. In Proceedings of the eleventh European conference on artificial intelligence (ECAI‘94) (pp. 341–345).

  • Nguen, N.T. (2008a). Inconsistency of knowledge and collective intelligence. Cybernetics & Systems, 39(6), 542–562.

    Article  Google Scholar 

  • Nguen, N.T. (2008b). Advanced methods for inconsistent knowledge management. Springer series: advanced information and knowledge processing. New York/Heidelberg/Berlin: Springer.

    Book  Google Scholar 

  • Nuseibeh, B., Easterbrook, S., Russo, A. (2001). Making inconsistency respectable in software development. Journal of Systems and Software, 58(2), 171–180.

    Article  Google Scholar 

  • Papini, O. (1992). A complete revision function in propositional calculus. In Proceedings of 10th European conference on artificial intelligence (ECAI‘92).

  • Partridge, D., & Wilks, Y. (1990). The foundations of artificial intelligence. Cambridge: Cambridge University Press.

    Book  Google Scholar 

  • Pollock, J.L., & Gillies, A. (2000). Belief revision and epistemology. Synthesizer, 122, 69–92.

    Article  MathSciNet  Google Scholar 

  • Priest, G., Routley, R., Norman, J. (Eds.) (1989). Paraconsistent logic: Essays on the inconsistent. München: Philosophia Verlag.

    Google Scholar 

  • Rescher, N. (1976). Plausible reasoning: an introduction to the theory and practice of plausibilistic inference. Amsterdam: Van Gorcum, Assen.

    Google Scholar 

  • Rescher, N., & Manor, R. (1970). On inference from inconsistent premises. Theory Decision, 1(2), 179–217.

    Article  Google Scholar 

  • Ross, T.J. (1994). Fuzzy logic with engineering applications. McGraw-Hill P.C.

  • Routley, R., Plumwood, V., Meyer, R.K., Brady, R.T. (1982). Relevant logics and their rivals. Atascadero, CA: Ridgeview.

    Google Scholar 

  • Schütte, K. (1960). Beweistheorie. Berlin: Springer-Verlag.

    Google Scholar 

  • Schwanke, R.W., & Kaiser, G.E. (1988). Living with inconsistency in large systems. In Proceedings of the international workshop on software version and configuration control, Grassau, Germany (pp. 98–118). Teubner, Stuttgart.

  • Shoenfield, J.R. (2001). Mathematical logic. Reading, MA: Addison-Wesley.

    Google Scholar 

  • Smolin, L. (1995). The Bekenstein bound, topological quantum field theory and pluralistic quantum field theory, Penn State preprint CGPG-95/8-7; Los Alamos Archives preprint in physics. arXiv:gr-qc/9508064. Accessed 23 Sept 2012.

  • Toulmin, S. (1956). The uses of argument. Cambridge: Cambridge University Press.

    Google Scholar 

  • VanPool, T.L. , VanPool, C.S. (Eds.) (2003). Essential tensions in archaeological method and theory. Salt Lake City: University of Utah Press.

    Google Scholar 

  • Wassermann, R. (2000). An algorithm for belief revision. In Proc. of 7th international conf. of principles of knowledge representation and reasoning (KR‘2000).

  • Weinzierl, A. (2010). Comparing inconsistency resolutions in multi-context systems. In M. Slavkovik (Ed.), Student session of the European summer school for logic, language, and information (pp. 17–24).

  • Williams, M.A. (1994). Transmutations of knowledge systems. In Proceedings of 4th international conference of principles of knowledge representation and reasoning (KR ‘94).

  • Williams, M.A. (1996). A practical approach to belief revision: Reason-based change. In Proceedings of 5th international conference of principles of knowledge representation and reasoning (KR‘96) (pp. 412–421).

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, UCLA, Los Angeles, CA, 90095, USA

    M. Burgin

  2. Centre for Law & ICT, University of Groningen, P.O. Box 716, 9700 AS, Groningen, The Netherlands

    C. N. J. de Vey Mestdagh

Authors
  1. M. Burgin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. C. N. J. de Vey Mestdagh
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to C. N. J. de Vey Mestdagh.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Burgin, M., de Vey Mestdagh, C.N.J. Consistent structuring of inconsistent knowledge. J Intell Inf Syst 45, 5–28 (2015). https://doi.org/10.1007/s10844-013-0270-7

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10844-013-0270-7

Keywords

Search

Navigation