Abstract
The well-founded model for any general deductive database computed using the paraconsistent relational model, based on four-valued logic, does not support inference rules such as disjunctive syllogism. In order to support disjunctive syllogism, we utilize the generalization of the relational model to quasi-classic (QC) logic, whose inference power is much closer to classical logic. As the paraconsistent relational model is capable of representing incomplete and inconsistent data, we propose an algorithm to find QC model for inconsistent positive extended disjunctive deductive databases. We also provide the proof for the algorithm.
Similar content being viewed by others
References
Alcântara, J., Damásio, C.V., Pereira, L.M.: Paraconsistent Logic Programs. In: Logics in Artificial Intelligence, pp. 345–356. Springer (2002)
Alcântara, J., Damásio, C. V., Pereira, L.M.: A Declarative Characterisation of Disjunctive Paraconsistent Answer Sets. In: ECAI. vol. 16, pp. 951. Citeseer (2004)
Alcântara, J., Damásio, C. V., Pereira, L.M.: An encompassing framework for paraconsistent logic programs. J. Appl. Log. 3(1), 67–95 (2005)
Arieli, O.: Paraconsistent declarative semantics for extended logic programs. Ann. Math. Artif. Intell. 36(4), 381–417 (2002)
Arieli, O.: Distance-based paraconsistent logics. Int. J. Approx. Reason. 48(3), 766–783 (2008)
Bagai, R.: Tuple Relational Calculus for Paraconsistent Databases. In: Advances in Artificial Intelligence, pp. 409–416. Springer (2000)
Bagai, R., Sunderraman, R.: A paraconsistent relational data model. Int. J. Comput. Math. 55(1-2), 39–55 (1995)
Bagai, R., Sunderraman, R.: Bottom-up computation of the fitting model for general deductive databases. J. Intell. Inf. Syst. 6(1), 59–75 (1996)
Bagai, R., Sunderraman, R.: Computing the well-founded model of deductive databases. Int. J. Uncertainty Fuzziness Knowledge Based Syst. 4(02), 157–175 (1996)
Barceló, P., Bertossi, L.: Logic Programs for Querying Inconsistent Databases. In: Practical Aspects of Declarative Languages, pp. 208–222. Springer (2003)
Belnap, Jr, N.D.: A Useful Four-Valued Logic. In: Modern Uses of Multiple-Valued Logic, pp. 5–37. Springer (1977)
Blair, H.A., Subrahmanian, V.: Paraconsistent logic programming. Theor. Comput. Sci. 68(2), 135–154 (1989)
Carnielli, W., Coniglio, M.E., Marcos, J.: Logics of Formal Inconsistency. In: Handbook of Philosophical Logic, pp. 1–93. Springer (2007)
Chazarain, J., Riscos, A., Alonso, J., Briales, E.: Multi-valued logic and gröner bases with applications to modal logic. J. Symb. Comput. 11(3), 181–194 (1991)
Damásio, C. V., Pereira, L.M.: A Survey of Paraconsistent Semantics for Logic Programs. In: Reasoning with Actual and Potential Contradictions, pp. 241–320. Springer (1998)
Galindo, M.J.O., Ramírez, J.R.A., Carballido, J.L.: Logical weak completions of paraconsistent logics. J. Log. Comput. 18(6), 913–940 (2008). doi:10.1093/logcom/exn015
Gelfond, M., Lifschitz, V.: Classical negation in logic programs and disjunctive databases. N. Gener. Comput. 9(3-4), 365–385 (1991)
Greco, G., Greco, S., Zumpano, E.: A logical framework for querying and repairing inconsistent databases. IEEE Trans. Knowl. Data Eng. 15(6), 1389–1408 (2003)
Greco, S., Zumpano, E.: Querying Inconsistent Databases. In: Logic for Programming and Automated Reasoning. pp. 308–325. Springer (2000)
Hunter, A.: Paraconsistent logics handbook of defeasible reasoning and uncertainty management systems: volume 2: reasoning with actual and potential contradictions (1998)
Hunter, A.: Reasoning with contradictory information using quasi-classical logic. J. Log. Comput. 10(5), 677–703 (2000)
Jayakumar, B., Sunderraman, R.: Paraconsistent relational model: a quasi-classic logic approach. In: IJCAI Workshop. vol. 13, pp. 82–90 (2015)
Klir, G., Yuan, B.: Fuzzy sets and fuzzy logic, vol. 4. Prentice Hall, New Jersey (1995)
Mayatskiy, N., Odintsov, S.P.: On deductive bases for paraconsistent answer set semantics. Journal of Applied Non-Classical Logics 23(1-2), 131–146 (2013)
Mendel, J.M.: Uncertain rule-based fuzzy logic system: introduction and new directions (2001)
Minker, J., Ruiz, C.: Semantics for disjunctive logic programs with explicit and default negation. Fundamenta Informaticae 20(1, 2, 3), 145–192 (1994)
Molinaro, C., Chomicki, J., Marcinkowski, J.: Disjunctive databases for representing repairs. Ann. Math. Artif. Intell. 57(2), 103–124 (2009)
Osorio, M., Pérez, J.A.N., Ramírez, J.R.A., Macías, V.B.: Logics with common weak completions. J. Log. Comput. 16(6), 867–890 (2006). doi:10.1093/logcom/exl013
Osorio, M., Zepeda, C., Nieves, J.C., Carballido, J.L.: G’3-stable semantics and inconsistency. Computación y Sistemas 13(1), 75–86 (2009)
Poole, D.: What the lottery paradox tells us about default reasoning. KR 89, 333–340 (1989)
Ricca, F., Faber, W., Leone, N.: A backjumping technique for disjunctive logic programming. AI Commun. 19(2), 155–172 (2006)
Sakama, C., Inoue, K.: Paraconsistent stable semantics for extended disjunctive programs. J. Log. Comput. 5(3), 265–285 (1995)
Subrahmanian, V.: Paraconsistent Disjunctive Deductive Databases. In: Proceedings of the Twentieth International Symposium on Multiple-Valued Logic, 1990. pp. 339–346. IEEE (1990)
Subrahmanian, V.: Paraconsistent disjunctive deductive databases. Theor. Comput. Sci. 93(1), 115–141 (1992)
Sunderraman, R.: Modeling Negative and Disjunctive Information in Relational Databases. In: Database and Expert Systems Applications. pp. 337–346. Springer (1997)
Zhang, X., Xiao, G., Lin, Z., Van den Bussche, J.: Inconsistency-tolerant reasoning with owl dl. Int. J. Approx. Reason. 55(2), 557–584 (2014)
Zhang, Z., Lin, Z., Ren, S.: Quasi-Classical Model Semantics for Logic Programs–A Paraconsistent Approach. In: Foundations of Intelligent Systems, pp. 181–190. Springer (2009)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Jayakumar, B., Sunderraman, R. Quasi-classical reasoning in paraconsistent databases. Ann Math Artif Intell 82, 131–159 (2018). https://doi.org/10.1007/s10472-017-9536-z
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10472-017-9536-z