×

zbMATH — the first resource for mathematics

Inconsistency measurement. (English) Zbl 1440.68278
Ben Amor, Nahla (ed.) et al., Scalable uncertainty management. 13th international conference, SUM 2019, Compiègne, France, December 16–18, 2019. Proceedings. Cham: Springer. Lect. Notes Comput. Sci. 11940, 9-23 (2019).
Summary: The field of Inconsistency Measurement is concerned with the development of principles and approaches to quantitatively assess the severity of inconsistency in knowledge bases. In this survey, we give a broad overview on this field by outlining its basic motivation and discussing some of these core principles and approaches. We focus on the work that has been done for classical propositional logic but also give some pointers to applications on other logical formalisms.
For the entire collection see [Zbl 1428.68006].
MSC:
68T27 Logic in artificial intelligence
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Baroni, P., Gabbay, D., Giacomin, M., van der Torre, L. (eds.): Handbook of Formal Argumentation. College Publications, London (2018) · Zbl 1395.03005
[2] Bertossi, L.: Repair-based degrees of database inconsistency. In: Balduccini, M., Lierler, Y., Woltran, S. (eds.) LPNMR 2019. LNCS, vol. 11481, pp. 195-209. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-20528-7_15 · Zbl 07115975
[3] Besnard, P.: Revisiting postulates for inconsistency measures. In: Fermé, E., Leite, J. (eds.) JELIA 2014. LNCS (LNAI), vol. 8761, pp. 383-396. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-11558-0_27 · Zbl 1432.68427
[4] Besnard, P.: Forgetting-based inconsistency measure. In: Schockaert, S., Senellart, P. (eds.) SUM 2016. LNCS (LNAI), vol. 9858, pp. 331-337. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-45856-4_23 · Zbl 1366.68278
[5] Besnard, P.: Basic postulates for inconsistency measures. In: Hameurlain, A., Küng, J., Wagner, R., Decker, H. (eds.) Transactions on Large-Scale Data- and Knowledge-Centered Systems XXXIV. LNCS, vol. 10620, pp. 1-12. Springer, Heidelberg (2017). https://doi.org/10.1007/978-3-662-55947-5_1
[6] Béziau, J.-Y., Carnielli, W., Gabbay, D. (eds.): Handbook of Paraconsistency. College Publications, London (2007) · Zbl 1206.03030
[7] Brachman, R.J., Levesque, H.J.: Knowledge Representation and Reasoning. Morgan Kaufmann Publishers, Massachusetts (2004) · Zbl 1341.68228
[8] Brewka, G., Eiter, T., Truszczynski, M.: Answer set programming at a glance. Commun. ACM 54(12), 92-103 (2011)
[9] Brewka, G., Thimm, M., Ulbricht, M.: Strong inconsistency. Artif. Intell. 267, 78-117 (2019) · Zbl 07099173
[10] Cholvy, L., Hunter, A.: Information fusion in logic: a brief overview. In: Gabbay, D.M., Kruse, R., Nonnengart, A., Ohlbach, H.J. (eds.) ECSQARU/FAPR -1997. LNCS, vol. 1244, pp. 86-95. Springer, Heidelberg (1997). https://doi.org/10.1007/BFb0035614
[11] Cholvy, L., Perrussel, L., Thevenin, J.M.: Using inconsistency measures for estimating reliability. Int. J. Approximate Reasoning 89, 41-57 (2017) · Zbl 1419.68187
[12] De Bona, G., Finger, M., Potyka, N., Thimm, M.: Inconsistency measurement in probabilistic logic. In: Measuring Inconsistency in Information, College Publications (2018) · Zbl 1451.68259
[13] De Bona, G., Grant, J., Hunter, A., Konieczny, S.: Towards a unified framework for syntactic inconsistency measures. In: Proceedings of AAAI 2018 (2018)
[14] Decker, H., Misra, S.: Database inconsistency measures and their applications. In: Damaševičius, R., Mikašytė, V. (eds.) ICIST 2017. CCIS, vol. 756, pp. 254-265. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-67642-5_21
[15] Gelfond, M., Leone, N.: Logic programming and knowledge representation - the a-prolog perspective. Artif. Intell. 138(1-2), 3-38 (2002) · Zbl 0995.68022
[16] Grant, J., Hunter, A.: Analysing inconsistent first-order knowledgebases. Artif. Intell. 172(8-9), 1064-1093 (2008) · Zbl 1183.68614
[17] Grant, J., Hunter, A.: Measuring consistency gain and information loss in stepwise inconsistency resolution. In: Liu, W. (ed.) ECSQARU 2011. LNCS (LNAI), vol. 6717, pp. 362-373. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-22152-1_31 · Zbl 1341.68256
[18] Grant, J., Hunter, A.: Analysing inconsistent information using distance-based measures. Int. J. Approximate Reasoning 89, 3-26 (2017) · Zbl 1419.68144
[19] Grant, J., Martinez, M.V. (eds.): Measuring Inconsistency in Information. College Publications, London (2018) · Zbl 1411.68015
[20] Grant, J.: Classifications for inconsistent theories. Notre Dame J. Form. Log. 19(3), 435-444 (1978) · Zbl 0305.02040
[21] Hansson, S.O.: A Textbook of Belief Dynamics. Kluwer Academic Publishers, Dordrecht (2001)
[22] Hunter, A., Konieczny, S.: Approaches to measuring inconsistent information. In: Bertossi, L., Hunter, A., Schaub, T. (eds.) Inconsistency Tolerance. LNCS, vol. 3300, pp. 191-236. Springer, Heidelberg (2005). https://doi.org/10.1007/978-3-540-30597-2_7 · Zbl 1111.68125
[23] Hunter, A., Konieczny, S.: Shapley inconsistency values. In: Proceedings of KR 2006, pp. 249-259 (2006)
[24] Hunter, A., Konieczny, S.: Measuring inconsistency through minimal inconsistent sets. In: Proceedings of KR 2008, pp. 358-366 (2008)
[25] Jabbour, S., Ma, Y., Raddaoui, B.: Inconsistency measurement thanks to MUS decomposition. In: Proceedings of AAMAS 2014, pp. 877-884 (2014)
[26] Jabbour, S.: On inconsistency measuring and resolving. In: Proceedings of ECAI 2016, pp. 1676-1677 (2016)
[27] Knight, K.M.: Measuring inconsistency. J. Philos. Log. 31, 77-98 (2001) · Zbl 1003.03022
[28] Konieczny, S., Pino Pérez, R.: On the logic of merging. In: Proceedings of KR 1998 (1998) · Zbl 1233.03024
[29] Ma, Y., Hitzler, P. : Distance-based measures of inconsistency and incoherency for description logics. In: Proceedings of DL 2010 (2010)
[30] Ma, Y., Qi, G., Xiao, G., Hitzler, P., Lin, Z.: An anytime algorithm for computing inconsistency measurement. In: Karagiannis, D., Jin, Z. (eds.) KSEM 2009. LNCS (LNAI), vol. 5914, pp. 29-40. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-10488-6_7
[31] Ma, Y., Qi, G., Xiao, G., Hitzler, P., Lin, Z.: Computational complexity and anytime algorithm for inconsistency measurement. Int. J. Softw. Inform. 4(1), 3-21 (2010)
[32] McAreavey, K., Liu, W., Miller, P.: Computational approaches to finding and measuring inconsistency in arbitrary knowledge bases. Int. J. Approximate Reasoning 55, 1659-1693 (2014) · Zbl 1309.68181
[33] Potyka, N., Thimm, M.: Inconsistency-tolerant reasoning over linear probabilistic knowledge bases. Int. J. Approximate Reasoning 88, 209-236 (2017) · Zbl 1418.68209
[34] Reiter, R.: A logic for default reasoning. Artif. Intell. 13, 81-132 (1980) · Zbl 0435.68069
[35] Thimm, M., Wallner, J. P.: Some complexity results on inconsistency measurement. In: Proceedings of KR 2016, pp. 114-123 (2016)
[36] Thimm, M.: On the expressivity of inconsistency measures. Artif. Intell. 234, 120-151 (2016) · Zbl 1352.68236
[37] Thimm, M.: Stream-based inconsistency measurement. Int. J. Approximate Reasoning 68, 68-87 (2016) · Zbl 1346.68189
[38] Thimm, M.: Measuring inconsistency with many-valued logics. Int. J. Approximate Reasoning 86, 1-23 (2017) · Zbl 1419.68134
[39] Thimm, M.: On the compliance of rationality postulates for inconsistency measures: a more or less complete picture. Künstliche Intell. 31(1), 31-39 (2017)
[40] Thimm, M.: The tweety library collection for logical aspects of artificial intelligence and knowledge representation. Künstliche Intell. 31(1), 93-97 (2017)
[41] Thimm, M.: On the evaluation of inconsistency measures. In: Measuring Inconsistency in Information. College Publications (2018) · Zbl 07088148
[42] Ulbricht, M., Thimm, M., Brewka, G.: Inconsistency measures for disjunctive logic programs under answer set semantics. In: Measuring Inconsistency in Information. College Publications (2018) · Zbl 07088150
[43] Ulbricht, M., Thimm, M., Brewka, G.: Measuring strong inconsistency. In: Proceedings of AAAI 2018, pp. 1989-1996 (2018) · Zbl 07099173
[44] Xiao, G., Ma, Y.: Inconsistency measurement based on variables in minimal unsatisfiable subsets. In: Proceedings of ECAI 2012 (2012) · Zbl 1327.68263
[45] Zhou, L.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.