A Comparison of Paraconsistent Description Logics

ABSTRACT

Description logics (DLs) are a family of logic-based knowledge representation formalisms with a number of computer science applications. DLs are especially well-known to be valuable for obtaining logical foundations of web ontology languages (e.g., W3C’s ontology language OWL). Paraconsistent (or inconsistency-tolerant) description logics (PDLs) have been studied to cope with inconsistencies which may frequently occur in an open world. In this paper, a comparison and survey of PDLs is presented. It is shown that four existing paraconsistent semantics (*i.e*., four-valued semantics, quasi-classical semantics, single-interpretation semantics and dual-interpretation semantics) for PDLs are essentially the same semantics. To show this, two generalized and extended new semantics are introduced, and an equivalence between them is proved.

Cite this paper

N. Kamide, "A Comparison of Paraconsistent Description Logics,"*International Journal of Intelligence Science*, Vol. 3 No. 2, 2013, pp. 99-109. doi: 10.4236/ijis.2013.32011.

N. Kamide, "A Comparison of Paraconsistent Description Logics,"

References

[1] N. Kamide, “Paraconsistent Semantics for Description Logics: A Comparison,” Proceedings of the 15th International Conference on Knowledge-Based and Intelligent Information and Engineering Systems, Lecture Notes in Artificial Intelligence, Vol. 6881, 2011, pp. 599-608.

[2] F. Baader, D. Calvanese, D. McGuinness, D. Nardi and P. F. Patel-Schneider, “The Description Logic Handbook: Theory, Implementation and Applications,” Cambridge University Press, Cambridge, 2003.

[3] M. Schmidt-Schauss and G. Smolka, “Attributive Concept Descriptions with Complements,” Artificial Intelligence, Vol. 48, 1991, pp. 1-26. doi:10.1016/0004-3702(91)90078-X

[4] Y. Ma, P. Hitzler and Z. Lin, “Algorithms for Paraconsistent Reasoning with OWL,” Proceedings of the 4th European Semantic Web Conference, Lecture Notes in Computer Science, Vol. 4519, 2007, pp. 399-413.

[5] Y. Ma, P. Hitzler and Z. Lin, “Paraconsistent Reasoning for Expressive and Tractable Description Logics,” Proceedings of the 21st International Workshop on Description Logic, Technical University of Aachen (RWTH), Aachen, 2008.

[6] C. Meghini and U. Straccia, “A Relevance Terminological Logic for Information Retrieval,” Proceedings of the 19th Annual International ACM SIGIR Conference on Research and Development in Information Retrieval, New York, 1996, pp. 197-205. doi:10.1145/243199.243267

[7] C. Meghini, F. Sebastiani and U. Straccia, “Mirlog: A Logic for Multimedia Information Retrieval,” Uncertainty and Logics: Advanced Models for the Representation and Retrieval of Information, Kluwer Academic Publishing, Dordrecht, 1998, pp. 151-185.

[8] S. P. Odintsov and H. Wansing, “Inconsistency-Tolerant Description Logic: Motivation and Basic Systems,” In: V. F. Hendricks and J. Malinowski, Eds., Trends in Logic: 50 Years of Studia Logica, Kluwer Academic Publishers, Dordrecht, 2003, pp. 301-335. doi:10.1007/978-94-017-3598-8_11

[9] S. P. Odintsov and H. Wansing, “Inconsistency-Tolerant Description Logic. Part II: Tableau Algorithms,” Journal of Applied Logic, Vol. 6, No. 3, 2008, pp. 343-360. doi:10.1016/j.jal.2007.06.001

[10] P. F. Patel-Schneider, “A Four-Valued Semantics for Terminological Logics,” Artificial Intelligence, Vol. 38, No. 3, 1989, pp. 319-351. doi:10.1016/0004-3702(89)90036-2

[11] U. Straccia, “A Sequent Calculus for Reasoning in Four-Valued Description Logics,” Proceedings of International Conference on Automated Reasoning with Analytic Tableaux and Related Methods, Lecture Notes in Computer Science, Vol. 1227, 1997, pp. 343-357.

[12] X. Zhang and Z. Lin, “Paraconsistent Reasoning with Quasi-Classical Semantics in ALC,” Proceedings of the 2nd International Conference on Web Reasoning and Rule Systems, Lecture Notes in Computer Science, Vol. 5341, 2008, pp. 222-229.

[13] X. Zhang, G. Qi, Y. Ma and Z. Lin, “Quasi-Classical Semantics for Expressive Description Logics,” Proceedings of the 22nd International Workshop on Description Logic, Vol. 477, Technical University of Aachen, Aachen, 2009.

[14] N. Kamide, “Paraconsistent Description Logics Revisited,” Proceedings of the 23rd International Workshop on Description Logics, Vol. 573, Technical University of Aachen, 2010, 12 p.

[15] N. Kamide, “Embedding-Based Approaches to Paraconsistent and Temporal Description Logics,” Journal of Logic and Computation, Vol. 22, No. 5, 2012, pp. 1097-1124. doi:10.1093/logcom/exr016

[16] K. Kaneiwa, “Description Logics with Contraries, Contradictories, and Subcontraries,” New Generation Computting, Vol. 25, No. 4, 2007, pp. 443-468. doi:10.1007/s00354-007-0028-2

[17] G. Wagner, “A Database Needs Two Kinds of Negations,” Proceeding of the 3rd Symposium on Mathematical Fundamentals of Database and Knowledge Bases Systems, Lecture Notes in Computer Science, Vol. 495, 1991, pp. 357-371.

[18] A. Almukdad and D. Nelson, “Constructible Falsity and Inexact Predicates,” Journal of Symbolic Logic, Vol. 49, 1984, pp. 231-233. doi:10.2307/2274105

[19] D. Nelson, “Constructible Falsity,” Journal of Symbolic Logic, Vol. 14, 1949, pp. 16-26. doi:10.2307/2268973

[20] N. Kamide, “An Embedding-Based Completeness Proof for Nelson’s Paraconsistent Logic,” Bulletin of the Section of Logic, Vol. 39, No. 3-4, 2010, pp. 205-214.

[21] S. P. Odintsov, “Algebraic Semantics for Paraconsistent Nelson’s Logic,” Journal of Logic and Computation, Vol. 13, No. 4, 2003, pp. 453-468. doi:10.1093/logcom/13.4.453

[22] H. Wansing, “The Logic of Information Structures,” Lecture Notes in Artificial Intelligence, Vol. 681, 1993, pp. 1-163.

[23] N. Kamide, “A Compatible Approach to Temporal Description Logics,” Proceedings of the 23rd International Workshop on Description Logics, Vol. 573, Technical University of Aachen, 2010, 12 p.

[24] A. N. Prior, “Time and Modality,” Clarendon Press, Ox- ford, 1957.

[25] N. Kamide and H. Wansing, “Proof Theory of Nelson’s Paraconsistent Logic: A Uniform Perspective,” Theoretical Computer Science, Vol. 415, 2012, pp. 1-38. doi:10.1016/j.tcs.2011.11.001

[26] N. Kamide and H. Wansing, “Completeness and Cut-Elimination Theorems for Trilattice Logics,” Annals of Pure and Applied Logic, Vol. 162, No. 10, 2011, pp. 816-835. doi:10.1016/j.apal.2011.03.001

[27] N. Kamide and H. Wansing, “A Paraconsistent Linear-Time Temporal Logic,” Fundamenta Informaticae, Vol. 106, No. 1, 2011, pp. 1-23.

[28] K. Kaneiwa and N. Kamide, “Paraconsistent Computation Tree Logic,” New Generation Computing, Vol. 29, No. 4, 2011, pp. 391-408. doi:10.1007/s00354-009-0116-6

[29] N. Kamide and H. Wansing, “Combining Linear-Time Temporal Logic with Constructiveness and Paraconsistency,” Journal of Applied Logic, Vol. 8, 2010, pp. 33-61. doi:10.1016/j.jal.2009.06.001

[1] N. Kamide, “Paraconsistent Semantics for Description Logics: A Comparison,” Proceedings of the 15th International Conference on Knowledge-Based and Intelligent Information and Engineering Systems, Lecture Notes in Artificial Intelligence, Vol. 6881, 2011, pp. 599-608.

[2] F. Baader, D. Calvanese, D. McGuinness, D. Nardi and P. F. Patel-Schneider, “The Description Logic Handbook: Theory, Implementation and Applications,” Cambridge University Press, Cambridge, 2003.

[3] M. Schmidt-Schauss and G. Smolka, “Attributive Concept Descriptions with Complements,” Artificial Intelligence, Vol. 48, 1991, pp. 1-26. doi:10.1016/0004-3702(91)90078-X

[4] Y. Ma, P. Hitzler and Z. Lin, “Algorithms for Paraconsistent Reasoning with OWL,” Proceedings of the 4th European Semantic Web Conference, Lecture Notes in Computer Science, Vol. 4519, 2007, pp. 399-413.

[5] Y. Ma, P. Hitzler and Z. Lin, “Paraconsistent Reasoning for Expressive and Tractable Description Logics,” Proceedings of the 21st International Workshop on Description Logic, Technical University of Aachen (RWTH), Aachen, 2008.

[6] C. Meghini and U. Straccia, “A Relevance Terminological Logic for Information Retrieval,” Proceedings of the 19th Annual International ACM SIGIR Conference on Research and Development in Information Retrieval, New York, 1996, pp. 197-205. doi:10.1145/243199.243267

[7] C. Meghini, F. Sebastiani and U. Straccia, “Mirlog: A Logic for Multimedia Information Retrieval,” Uncertainty and Logics: Advanced Models for the Representation and Retrieval of Information, Kluwer Academic Publishing, Dordrecht, 1998, pp. 151-185.

[8] S. P. Odintsov and H. Wansing, “Inconsistency-Tolerant Description Logic: Motivation and Basic Systems,” In: V. F. Hendricks and J. Malinowski, Eds., Trends in Logic: 50 Years of Studia Logica, Kluwer Academic Publishers, Dordrecht, 2003, pp. 301-335. doi:10.1007/978-94-017-3598-8_11

[9] S. P. Odintsov and H. Wansing, “Inconsistency-Tolerant Description Logic. Part II: Tableau Algorithms,” Journal of Applied Logic, Vol. 6, No. 3, 2008, pp. 343-360. doi:10.1016/j.jal.2007.06.001

[10] P. F. Patel-Schneider, “A Four-Valued Semantics for Terminological Logics,” Artificial Intelligence, Vol. 38, No. 3, 1989, pp. 319-351. doi:10.1016/0004-3702(89)90036-2

[11] U. Straccia, “A Sequent Calculus for Reasoning in Four-Valued Description Logics,” Proceedings of International Conference on Automated Reasoning with Analytic Tableaux and Related Methods, Lecture Notes in Computer Science, Vol. 1227, 1997, pp. 343-357.

[12] X. Zhang and Z. Lin, “Paraconsistent Reasoning with Quasi-Classical Semantics in ALC,” Proceedings of the 2nd International Conference on Web Reasoning and Rule Systems, Lecture Notes in Computer Science, Vol. 5341, 2008, pp. 222-229.

[13] X. Zhang, G. Qi, Y. Ma and Z. Lin, “Quasi-Classical Semantics for Expressive Description Logics,” Proceedings of the 22nd International Workshop on Description Logic, Vol. 477, Technical University of Aachen, Aachen, 2009.

[14] N. Kamide, “Paraconsistent Description Logics Revisited,” Proceedings of the 23rd International Workshop on Description Logics, Vol. 573, Technical University of Aachen, 2010, 12 p.

[15] N. Kamide, “Embedding-Based Approaches to Paraconsistent and Temporal Description Logics,” Journal of Logic and Computation, Vol. 22, No. 5, 2012, pp. 1097-1124. doi:10.1093/logcom/exr016

[16] K. Kaneiwa, “Description Logics with Contraries, Contradictories, and Subcontraries,” New Generation Computting, Vol. 25, No. 4, 2007, pp. 443-468. doi:10.1007/s00354-007-0028-2

[17] G. Wagner, “A Database Needs Two Kinds of Negations,” Proceeding of the 3rd Symposium on Mathematical Fundamentals of Database and Knowledge Bases Systems, Lecture Notes in Computer Science, Vol. 495, 1991, pp. 357-371.

[18] A. Almukdad and D. Nelson, “Constructible Falsity and Inexact Predicates,” Journal of Symbolic Logic, Vol. 49, 1984, pp. 231-233. doi:10.2307/2274105

[19] D. Nelson, “Constructible Falsity,” Journal of Symbolic Logic, Vol. 14, 1949, pp. 16-26. doi:10.2307/2268973

[20] N. Kamide, “An Embedding-Based Completeness Proof for Nelson’s Paraconsistent Logic,” Bulletin of the Section of Logic, Vol. 39, No. 3-4, 2010, pp. 205-214.

[21] S. P. Odintsov, “Algebraic Semantics for Paraconsistent Nelson’s Logic,” Journal of Logic and Computation, Vol. 13, No. 4, 2003, pp. 453-468. doi:10.1093/logcom/13.4.453

[22] H. Wansing, “The Logic of Information Structures,” Lecture Notes in Artificial Intelligence, Vol. 681, 1993, pp. 1-163.

[23] N. Kamide, “A Compatible Approach to Temporal Description Logics,” Proceedings of the 23rd International Workshop on Description Logics, Vol. 573, Technical University of Aachen, 2010, 12 p.

[24] A. N. Prior, “Time and Modality,” Clarendon Press, Ox- ford, 1957.

[25] N. Kamide and H. Wansing, “Proof Theory of Nelson’s Paraconsistent Logic: A Uniform Perspective,” Theoretical Computer Science, Vol. 415, 2012, pp. 1-38. doi:10.1016/j.tcs.2011.11.001

[26] N. Kamide and H. Wansing, “Completeness and Cut-Elimination Theorems for Trilattice Logics,” Annals of Pure and Applied Logic, Vol. 162, No. 10, 2011, pp. 816-835. doi:10.1016/j.apal.2011.03.001

[27] N. Kamide and H. Wansing, “A Paraconsistent Linear-Time Temporal Logic,” Fundamenta Informaticae, Vol. 106, No. 1, 2011, pp. 1-23.

[28] K. Kaneiwa and N. Kamide, “Paraconsistent Computation Tree Logic,” New Generation Computing, Vol. 29, No. 4, 2011, pp. 391-408. doi:10.1007/s00354-009-0116-6

[29] N. Kamide and H. Wansing, “Combining Linear-Time Temporal Logic with Constructiveness and Paraconsistency,” Journal of Applied Logic, Vol. 8, 2010, pp. 33-61. doi:10.1016/j.jal.2009.06.001