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.
References
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
Andreka H, Ryan M, Schobbens PY (2002) Operators and laws for combining preference relations. J Logic Comput 12(1):13–53
Arenas M, Bertossi LE, Chomicki J (1999) Consistent query answers in inconsistent databases. In: Proc. of PODS, pp 68–79
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
Bell DA, Qi G, Liu W (2007) Approaches to inconsistency handling in description-logic based ontologies. In: OTM workshops, (2), pp 1303–1311
Besnard P, Hunter A (2008) Elements of argumentation. MIT Press, Cambridge
Bienvenu M (2011) First-order expressibility results for queries over inconsistent DL-Lite knowledge bases. In: Proc. of DL
Bienvenu M (2012) On the complexity of consistent query answering in the presence of simple ontologies. In: Proc. of AAAI, pp 705–711
Borgida A, Walsh TJ, Hirsh H (2005) Towards measuring similarity in description logics. In: Proc. of DL
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
Chomicki J (2007) Consistent query answering: five easy pieces. In: Proc. of ICDT, pp 1–17
da Costa PCG, Laskey KB (2006) PR-OWL: a framework for probabilistic ontologies. In: Proc. of FOIS, pp 237–249
Dubois D, Prade H (1994) Can we enforce full compositionality in uncertainty calculi? In: Proc. of AAAI, pp 149–154
Dubois D, Prade H (2001) Possibility theory, probability theory and multiple-valued logics: a clarification. Ann Math Artif Intell 32(1–4):35–66
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
Fermé E, Hansson S (2011) AGM 25 years: twenty-five years of research in belief change. J Philos Logic 40(2):295–331
Gärdenfors P (1988) Knowledge in flux: modeling the dynamics of epistemic states. MIT Press, Cambridge
Gärdenfors P (1992) Belief revision and nonmonotonic logic: two sides of the same coin? In: Proc. of ECAI, pp 768–773
Gärdenfors P, Makinson D (1988) Revisions of knowledge systems using epistemic entrenchment. In: Proc. of TARK, pp 83–95
Gebser M, Kaminski R, Kaufmann B, Schaub T (2013) Answer set solving in practice. Morgan and Claypool, San Rafael
Gelfond M, Leone N (2002) Logic programming and knowledge representation–the A-Prolog perspective. Artif Intell 138:3–38
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
Hansson S (1999) A textbook of belief dynamics. Kluwer Academic Publishers, Dordrecht
Heinsohn J (1994) Probabilistic description logics. In: Proc. of UAI, pp 311–318
Horrocks I, Sattler U, Tobies S (2000) Reasoning with individuals for the description logic \({\cal{SHIQ}}\). In: Proc. of CADE, pp 482–496
Jaeger M (1994) Probabilistic reasoning in terminological logics. In: Proc. of KR, pp 305–316
Jaynes E (1983) Papers on probability, statistics and statistical physics. D. Reidel Publishing Company, Dordrecht
Jung JC, Lutz C (2012) Ontology-based access to probabilistic data with OWL QL. In: Proc. of ISWC, part I, pp 182–197
Kern-Isberner G (2001) Conditionals in nonmonotonic reasoning and belief revision. In: LNAI 2087. Springer, Berlin
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
Koller D, Levy A, Pfeffer A (1997) P-Classic: a tractable probabilistic description logic. In: Proc. of AAAI, pp 390–397
Kraus S, Lehmann D, Magidor M (1990) Nonmonotonic reasoning, preferential models and cumulative logics. Artif Intell 44:167–207
Lakemeyer G, Erdem E, Kern-Isberner G, Schaub T (2015) Workshop on Hybrid reasoning at IJCAI-2015. https://www.hybrid-reasoning.org/ijcai15_ws
Lembo D, Lenzerini M, Rosati R, Ruzzi M, Savo DF (2010) Inconsistency-tolerant semantics for description logics. In: Proc. of RR, pp 103–117
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
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
Lukasiewicz T (2008) Expressive probabilistic description logics. Artif Intell 172(6/7):852–883
Lukasiewicz T, Martinez MV, Simari GI (2012) Inconsistency handling in Datalog+/– ontologies. In: Proc. of ECAI, pp 558–563
Lukasiewicz T, Straccia U (2008) Managing uncertainty and vagueness in description logics for the Semantic Web. J Web Semant 6(4):291–308
Lutz C, Schröder L (2010) Probabilistic description logics for subjective uncertainty. In: Proc. of KR, pp 393–403
Maedche A, Staab S (2002) Measuring similarity between ontologies. In: Proc. of EKAW, pp 251–263
Maier F, Ma Y, Hitzler P (2013) Paraconsistent OWL and related logics. Semant Web 4(4):395–427
Makinson D (1989) General theory of cumulative inference. In: Proc. of NMR, pp 1–18
McDermott D, Doyle J (1980) Non-monotonic logic I. Artif Intell 13:41–72
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
Neves R, Bonnefon J, Raufaste E (2002) An empirical test of patterns for nonmonotonic inference. Ann Math Artif Intell 34(1–3):107–130
Nguyen LA, Szalas A (2010) Three-valued paraconsistent reasoning for semantic web agents. In: Proc. of KES-AMSTA, pp 152–162
Paris J (1994) The uncertain reasoner’s companion—a mathematical perspective. Cambridge University Press, Cambridge
Paris J (1999) Common sense and maximum entropy. Synthese 117:75–93
Reiter R (1980) A logic for default reasoning. Artif Intell 13:81–132
Rosati R (2011) On the complexity of dealing with inconsistency in description logic ontologies. In: Proc. of IJCAI, pp 1057–1062
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
Spohn W (2012) the laws of belief: ranking theory and its philosophical applications. Oxford University Press, Oxford
Straccia U (2001) Reasoning within fuzzy description logics. J Artif Intell Res 14:137–166
Straccia U (2012) Top-k retrieval for ontology mediated access to relational databases. Inf Sci 198:1–23
Tresp C, Molitor R (1998) A description logic for vague knowledge. In: Proc. of ECAI, pp 361–365
van der Torre LWN (1999) Defeasible goals. In: Proc. of ECSQARU, pp 274–385
Yen J (1991) Generalizing term subsumption languages to fuzzy logic. In: Proc. of IJCAI, pp 472–477
Zadeh LA (1965) Fuzzy sets. Inf Control 8(3):338–353
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
Corresponding author
Rights and permissions
About this article
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
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13218-016-0480-6