Reasoning with inconsistent possibilistic description logics ontologies with disjunctive assertions

Authors

  • Sergio Alejandro Gómez Artificial Intelligence Research and Development Laboratory (LIDIA), Department of Computer Science and Engineering, Universidad Nacional del Sur, Bahía Blanca, Argentina

Keywords:

ontology reasoning, Suppositional argumentation, inconsistency handling, Possibilistic Description Logics, Semantic Web, Artificial Intelligence

Abstract

We present a preliminary framework for reasoning with possibilistic description logics ontologies with disjunctive assertions (PoDLoDA ontologies for short). Given a PoDLoDA ontology, its terminological box is expressed in the description logic programming fragment but its assertional box allows four kinds of statements: an individual is a member of a concept, two individuals are related through a role, an individual is a member of the union of two or more concepts or two individuals are related through the union of two or more roles. Axioms and statements in PoDLoDA ontologies have a numerical certainty degree attached. A disjunctive assertion expresses a doubt respect to the membership of either individuals to union of concepts or pairs of individuals to the union of roles. Because PoDLoDA ontologies allow to represent incomplete and potentially inconsistent information, instance checking is addressed through an adaptation of Bodanza’s Suppositional Argumentation System that allows to reason with modus ponens and constructive dilemmas. We think that our approach will be of use for implementers of reasoning systems in the Semantic Web where uncertainty of membership of individuals to concepts or roles is present.

Downloads

Download data is not yet available.

References

[1] Teresa Alsinet, Carlos Iván Chesñevar, and Lluis Godo. A level-based approach to computing warranted arguments in possibilistic defeasible logic programming. In Philippe Besnard, Sylvie Doutre, and Anthony Hunter, editors, COMMA, volume 172 of Frontiers in Artificial Intelligence and Applications, pages 1–12. IOS Press, 2008.
[2] Grigoris Antoniou and Antonis Bikakis. DR-Prolog: A System for Defeasible Reasoning with Rules and Ontologies on the Semantic Web. IEEE Transactions on Knowledge and Data Engineering, 19(2):233–245, 2007.
[3] Franz Baader, Diego Calvanese, Deborah McGuinness, Daniele Nardi, and Peter Patel-Schneider, editors. The Description Logic Handbook – Theory, Implementation and Applications. Cambridge University Press, 2003.
[4] Trevor J. M. Bench-Capon and Paul E. Dunne. Argumentation in artificial intelligence. Artificial Intelligence, 171(10-15):619–641, 2007.
[5] Salem Benferhat and Zied Bouraoui. Possibilistic DL-Lite. In Scalable Uncertainty Management, pages 346–359. Springer, 2013.
[6] Salem Benferhat and Zied Bouraoui. Min-based possibilistic dl-lite. Journal of Logic and Computation, 2015.
[7] Salem Benferhat, Zied Bouraoui, Sylvain Lagrue, and Julien Rossit. Merging Inconmensurable Possibilistic DL-Lite Assertional Bases. In Odile Papini, Salem Benferhat, Laurent Garcia, and Marie-Laure Mugnier, editors, Proceedings of the IJCAI Workshop 13 Ontologies and Logic Programming for Query Answering, pages 90–95, 2015.
[8] T. Berners-Lee, J. Hendler, and O. Lassila. The Semantic Web. Scientific American, 2001.
[9] Alexander Bochman. Collective Argumentation and Disjunctive Logic Programming. Journal of Logic and Computation, 13(3):405–428, 2003.
[10] Gustavo Bodanza. Disjunctions and Specificity in Suppositional Defeasible Argumentation. Logic Journal of the Interest Group in Pure and Applied Logics, 10(1):23–49, 2002.
[11] Martin Caminada and Leila Amgoud. On the evaluation of argumentation formalisms. Artificial Intelligence, 171:286–310, 2007.
[12] Carlos Iván Chesñevar, Ana Maguitman, and Ronald Loui. Logical Models of Argument. ACM Computing Surveys, 32(4):337–383, December 2000.
[13] D. Dubois, J. Mengin, and H. Prade. Possibilistic uncertainty and fuzzy features in description logic. A preliminary discussion. In E. Sanchez, editor, Fuzzy Logic and the Semantic Web. Capturing Intelligence, volume 1, pages 101–113. Elsevier, 2006.
[14] A. Garcı́a and G. Simari. Defeasible Logic Programming an Argumentative Approach. Theory and Practice of Logic Programming, 4(1):95–138, 2004.
[15] Michael Gelfond, Vladimir Lifschitz, Halina Przymusińska, and Mirolaw Truszczyński. Disjunctive Defaults. In Proc. 2nd Int. Conf. on Principles of Knowledge Representation and Reasoning, pages 230–237, 1991.
[16] Sergio A. Gómez, Carlos I Chesñevar, and Guillermo R. Simari. Using Possibilistic Defeasible Logic Programming for Reasoning with Inconsistent Ontologies. In Armando Di Giusti and Javier Diaz, editors, Computer Science & Technology Series. XVII Argentine Congress of Computer Science Selected Papers, pages 19–29, 2012.
[17] Sergio Alejandro Gómez, Carlos Iván Chesñevar, and Guillermo Ricardo Simari. Reasoning with Inconsistent Ontologies Through Argumentation. Applied Artificial Intelligence, 1(24):102–148, 2010.
[18] Sergio Alejandro Gómez, Carlos Iván Chesñevar, and Guillermo Ricardo Simari. ONTOarg: A Decision Support Framework for Ontology Integration based on Argumentation. Expert Systems with Applications, 40:1858–1870, 2013.
[19] Sergio Alejandro Gómez and Guillermo Ricardo Simari. Merging of ontologies using belief revision and defeasible logic programming. Inteligencia Artificial, 16(52):16–28, 2013.
[20] Benjamin N. Grosof, Ian Horrocks, Raphael Volz, and Stefan Decker. Description Logic Programs: Combining Logic Programs with Description Logics. WWW2003, May 20-24, Budapest, Hungary, 2003.
[21] B. Hollunder. An alternative proof method for possibilistic logic and its application to terminological logics. International Journal of Approximate Reasoning, 12(2):85–109, 1995.
[22] Zhisheng Huang, Frank van Harmelen, and Annette ten Teije. Reasoning with Inconsistent Ontologies. In Leslie Pack Kaelbling and Alessandro Saffiotti, editors, Proc. 19th International Joint Conference on Artificial Intelligence (IJCAI’05), pages 454–459, Edinburgh, Scotland, August 2005.
[23] Thomas Lukasiewicz. Expressive probabilistic description logics. Artificial Intelligence, 172:852–883, 2008.
[24] Martı́n O. Moguillansky and Marcelo A. Falappa. A non-monotonic Description Logics model for merging terminologies. Inteligencia Artificial, Revista Iberoamericana de Inteligencia Artificial, 11(35):77–88, 2007.
[25] Martı́n O. Moguillansky, Nicolás D. Rotstein, and Marcelo A. Falappa. Generalized Abstract Argumentation: A First-order Machinery towards Ontology Debugging. Inteligencia Artificial, 46:17–33, 2010.
[26] Juan Carlos Nieves, Mauricio Osorio, and Ulises Cortés. Semantics for Possibilistic Disjunctive Programs. Theory and Practice of Logic Programming (TPLP), 13(1):33–70, 2013.
[27] Iyad Rahwan and Guillermo R. Simari. Argumentation in Artificial Intelligence. Springer, 2009.
[28] Chiaki Sakama and Katsumi Inoue. Relating disjunctive logic programs to default theories. In Proceedings of the 2nd International Workshop on Logic Programming and Nonmonotonic Reasoning (LP-NMR’93), pages 266–282. MIT Press, 1993.
[29] Kewen Wang. Argumentation-based abduction in disjunctive logic programming, 2000.
[30] Kewen Wang and Lizhu Zhou. Comparisons and computation of well-founded semantics for disjunctive logic programs. ACM Trans. Comput. Logic, 6(2):295–327, April 2005.

Downloads

Published

2015-11-01

How to Cite

Gómez, S. A. (2015). Reasoning with inconsistent possibilistic description logics ontologies with disjunctive assertions. Journal of Computer Science and Technology, 15(02), p. 68–74. Retrieved from https://journal.info.unlp.edu.ar/JCST/article/view/552

Issue

Section

Original Articles