Skip to main content
Log in

Many Facets of Reasoning Under Uncertainty, Inconsistency, Vagueness, and Preferences: A Brief Survey

KI - Künstliche Intelligenz Aims and scope Submit manuscript

Abstract

In this paper, we give an introduction to reasoning under uncertainty, inconsistency, vagueness, and preferences in artificial intelligence (AI), including some historic notes and a brief survey to previous approaches.

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

Access this article

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

Instant access to the full article PDF.

Institutional subscriptions

References

  1. Alchourrón C, Gärdenfors P, Makinson D (1985) On the logic of theory change: partial meet contraction and revision functions. J Symb Logic 50(2):510–530

    Article  MathSciNet  MATH  Google Scholar 

  2. Andreka H, Ryan M, Schobbens PY (2002) Operators and laws for combining preference relations. J Logic Comput 12(1):13–53

    Article  MathSciNet  MATH  Google Scholar 

  3. Arenas M, Bertossi LE, Chomicki J (1999) Consistent query answers in inconsistent databases. In: Proc. of PODS, pp 68–79

  4. Baader F, Borgwardt S, Peñaloza R (2015) On the decidability status of fuzzy \({\cal{ALC}}\) with general concept inclusions. J Philos Logic 44(2):117–146

  5. Bell DA, Qi G, Liu W (2007) Approaches to inconsistency handling in description-logic based ontologies. In: OTM workshops, (2), pp 1303–1311

  6. Besnard P, Hunter A (2008) Elements of argumentation. MIT Press, Cambridge

    Book  Google Scholar 

  7. Bienvenu M (2011) First-order expressibility results for queries over inconsistent DL-Lite knowledge bases. In: Proc. of DL

  8. Bienvenu M (2012) On the complexity of consistent query answering in the presence of simple ontologies. In: Proc. of AAAI, pp 705–711

  9. Borgida A, Walsh TJ, Hirsh H (2005) Towards measuring similarity in description logics. In: Proc. of DL

  10. Brewka G, Ellmauthaler S, Gonçalves R, Knorr M, Leite J, Pührer J (2016) Inconsistency management in reactive multi-context systems. In: Proc. of JELIA, pp 529–535

  11. Chomicki J (2007) Consistent query answering: five easy pieces. In: Proc. of ICDT, pp 1–17

  12. da Costa PCG, Laskey KB (2006) PR-OWL: a framework for probabilistic ontologies. In: Proc. of FOIS, pp 237–249

  13. Dubois D, Prade H (1994) Can we enforce full compositionality in uncertainty calculi? In: Proc. of AAAI, pp 149–154

  14. Dubois D, Prade H (2001) Possibility theory, probability theory and multiple-valued logics: a clarification. Ann Math Artif Intell 32(1–4):35–66

    Article  MathSciNet  MATH  Google Scholar 

  15. Dung P (1995) On the acceptability of arguments and its fundamental role in nonmonotonic reasoning, logic programming and n-person games. Artif Intell 77:321–357

    Article  MathSciNet  MATH  Google Scholar 

  16. Fermé E, Hansson S (2011) AGM 25 years: twenty-five years of research in belief change. J Philos Logic 40(2):295–331

    Article  MathSciNet  MATH  Google Scholar 

  17. Gärdenfors P (1988) Knowledge in flux: modeling the dynamics of epistemic states. MIT Press, Cambridge

    MATH  Google Scholar 

  18. Gärdenfors P (1992) Belief revision and nonmonotonic logic: two sides of the same coin? In: Proc. of ECAI, pp 768–773

  19. Gärdenfors P, Makinson D (1988) Revisions of knowledge systems using epistemic entrenchment. In: Proc. of TARK, pp 83–95

  20. Gebser M, Kaminski R, Kaufmann B, Schaub T (2013) Answer set solving in practice. Morgan and Claypool, San Rafael

    MATH  Google Scholar 

  21. Gelfond M, Leone N (2002) Logic programming and knowledge representation–the A-Prolog perspective. Artif Intell 138:3–38

    Article  MathSciNet  MATH  Google Scholar 

  22. Haase P, Harmelen FV, Huang Z, Stuckenschmidt H, Sure Y (2005) A framework for handling inconsistency in changing ontologies. In: Proc. of ISWC, pp 353–367

  23. Hansson S (1999) A textbook of belief dynamics. Kluwer Academic Publishers, Dordrecht

    Book  MATH  Google Scholar 

  24. Heinsohn J (1994) Probabilistic description logics. In: Proc. of UAI, pp 311–318

  25. Horrocks I, Sattler U, Tobies S (2000) Reasoning with individuals for the description logic \({\cal{SHIQ}}\). In: Proc. of CADE, pp 482–496

  26. Jaeger M (1994) Probabilistic reasoning in terminological logics. In: Proc. of KR, pp 305–316

  27. Jaynes E (1983) Papers on probability, statistics and statistical physics. D. Reidel Publishing Company, Dordrecht

    MATH  Google Scholar 

  28. Jung JC, Lutz C (2012) Ontology-based access to probabilistic data with OWL QL. In: Proc. of ISWC, part I, pp 182–197

  29. Kern-Isberner G (2001) Conditionals in nonmonotonic reasoning and belief revision. In: LNAI 2087. Springer, Berlin

  30. Kern-Isberner G (2004) A thorough axiomatization of a principle of conditional preservation in belief revision. Ann Math Artif Intell 40(1/2):127–164

    Article  MathSciNet  MATH  Google Scholar 

  31. Koller D, Levy A, Pfeffer A (1997) P-Classic: a tractable probabilistic description logic. In: Proc. of AAAI, pp 390–397

  32. Kraus S, Lehmann D, Magidor M (1990) Nonmonotonic reasoning, preferential models and cumulative logics. Artif Intell 44:167–207

    Article  MathSciNet  MATH  Google Scholar 

  33. Lakemeyer G, Erdem E, Kern-Isberner G, Schaub T (2015) Workshop on Hybrid reasoning at IJCAI-2015. https://www.hybrid-reasoning.org/ijcai15_ws

  34. Lembo D, Lenzerini M, Rosati R, Ruzzi M, Savo DF (2010) Inconsistency-tolerant semantics for description logics. In: Proc. of RR, pp 103–117

  35. Lembo D, Lenzerini M, Rosati R, Ruzzi M, Savo DF (2011) Query rewriting for inconsistent DL-Lite ontologies. In: Proc. of RR, pp 155–169

  36. Leone N, Eiter T, Faber W, Calimeri F, Dell’Armi T, Eiter T, Gottlob G, Ianni G, Ielpa G, Koch C, Perri S, Polleres A (2002) The DLV system. In: Proc. of JELIA, pp 537–540

  37. Lukasiewicz T (2008) Expressive probabilistic description logics. Artif Intell 172(6/7):852–883

    Article  MathSciNet  MATH  Google Scholar 

  38. Lukasiewicz T, Martinez MV, Simari GI (2012) Inconsistency handling in Datalog+/– ontologies. In: Proc. of ECAI, pp 558–563

  39. Lukasiewicz T, Straccia U (2008) Managing uncertainty and vagueness in description logics for the Semantic Web. J Web Semant 6(4):291–308

    Article  Google Scholar 

  40. Lutz C, Schröder L (2010) Probabilistic description logics for subjective uncertainty. In: Proc. of KR, pp 393–403

  41. Maedche A, Staab S (2002) Measuring similarity between ontologies. In: Proc. of EKAW, pp 251–263

  42. Maier F, Ma Y, Hitzler P (2013) Paraconsistent OWL and related logics. Semant Web 4(4):395–427

    Google Scholar 

  43. Makinson D (1989) General theory of cumulative inference. In: Proc. of NMR, pp 1–18

  44. McDermott D, Doyle J (1980) Non-monotonic logic I. Artif Intell 13:41–72

    Article  MATH  Google Scholar 

  45. Moore R (1985) A formal theory of knowledge and action. In: Hobbs J, Moore R (eds) Formal theories of the commonsense world. Ablex Publishing Corporation, Norwood, pp 319–358

    Google Scholar 

  46. Neves R, Bonnefon J, Raufaste E (2002) An empirical test of patterns for nonmonotonic inference. Ann Math Artif Intell 34(1–3):107–130

    Article  MathSciNet  MATH  Google Scholar 

  47. Nguyen LA, Szalas A (2010) Three-valued paraconsistent reasoning for semantic web agents. In: Proc. of KES-AMSTA, pp 152–162

  48. Paris J (1994) The uncertain reasoner’s companion—a mathematical perspective. Cambridge University Press, Cambridge

  49. Paris J (1999) Common sense and maximum entropy. Synthese 117:75–93

    Article  MathSciNet  MATH  Google Scholar 

  50. Reiter R (1980) A logic for default reasoning. Artif Intell 13:81–132

    Article  MathSciNet  MATH  Google Scholar 

  51. Rosati R (2011) On the complexity of dealing with inconsistency in description logic ontologies. In: Proc. of IJCAI, pp 1057–1062

  52. Spohn W (1988) Ordinal conditional functions: a dynamic theory of epistemic states. In: Harper W, Skyrms B (eds) Causation in decision, belief change, and statistics, II. Kluwer Academic Publishers, Dordrecht, pp 105–134

  53. Spohn W (2012) the laws of belief: ranking theory and its philosophical applications. Oxford University Press, Oxford

  54. Straccia U (2001) Reasoning within fuzzy description logics. J Artif Intell Res 14:137–166

    MathSciNet  MATH  Google Scholar 

  55. Straccia U (2012) Top-k retrieval for ontology mediated access to relational databases. Inf Sci 198:1–23

    Article  MathSciNet  MATH  Google Scholar 

  56. Tresp C, Molitor R (1998) A description logic for vague knowledge. In: Proc. of ECAI, pp 361–365

  57. van der Torre LWN (1999) Defeasible goals. In: Proc. of ECSQARU, pp 274–385

  58. Yen J (1991) Generalizing term subsumption languages to fuzzy logic. In: Proc. of IJCAI, pp 472–477

  59. Zadeh LA (1965) Fuzzy sets. Inf Control 8(3):338–353

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

This work was partially supported by the UK EPSRC Grants EP/J008346/1, EP/L012138/1, and EP/M025268/1, and by The Alan Turing Institute under the EPSRC Grant EP/N510129/1.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Thomas Lukasiewicz.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kern-Isberner, G., Lukasiewicz, T. Many Facets of Reasoning Under Uncertainty, Inconsistency, Vagueness, and Preferences: A Brief Survey. Künstl Intell 31, 9–13 (2017). https://doi.org/10.1007/s13218-016-0480-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13218-016-0480-6

Keywords

Navigation