Abstract
Classical logic predicts that everything (thus nothing useful at all) follows from inconsistency. A paraconsistent logic is a logic where inconsistency does not lead to such an explosion, and since in practice consistency is dificult to achieve there are many potential applications of paraconsistent logics in query answering systems. We compare the paraconsistent and the non-monotonic solutions to the problem of contradictions. We propose a many-valued paraconsistent logic based on a simple notion of indeterminacy. In particular we describe the semantics of the logic using key equalities for the logical operators. We relate our approach to works on bilattices. We also discuss and provide formalizations of two case studies, notably the well-known example involving penguins and a more interesting example in the domain of medicine.
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References
J. M. Abe. Some recent applications of paraconsistent systems to AI. Logique & Analyse, 157:83–96, 1997.
R. Bagai. A query construct for paraconsistent databases. In International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, 428–434, 1998.
R. Bagai and R. Sunderraman. A paraconsistent relational data model. International Journal of Computer Mathematics, 55(1):39–55, 1995.
N. D. Belnap Jr. A useful four-valued logic. In J. M. Dunn and G. Epstein, editors, Modern Uses of Multiple-Valued Logic, pages 8–37. D. Reidel, 1977.
P. Besnard and A. Hunter. Introduction to actual and potential contradictions. In D. M. Gabbay and P. Smets, editors, Handbook of Defeasible Reasoning and Uncertainty Management Systems: Volume II, pages 1–9. Kluwer, 1989.
J.-Y. Béziau. What is paraconsistent logic? In D. Batens et al., editors, Frontiers in Paraconsistent Logic, pages 95–111. Research Studies Press, 2000.
E. J. Borowski and J. M. Borwein. Dictionary of Mathematics. Collins, 1989.
N. C. A. da Costa and V. S. Subrahmanian. Paraconsistent logics as a formalism for reasoning about inconsistent knowledge bases. Artificial Intelligence in Medicine, 1:167–174, 1989.
Hendrik Decker, Jørgen Villadsen, and Toshiharu Waragai, editors. Paraconsistent Computational Logic, volume 95 of Datalogiske Skrifter, Roskilde, Denmark, July 27, 2002. Roskilde University.
G. Evans. Can there be vague objects? Analysis, 38(4):208, 1978.
D. Gabbay and F. Guenthner, editors. Handbook of Philosophical Logic, Volume I: Elements of Classical Logic. D. Reidel, 1983.
M. Ginsberg. Readings in Nonmonotonic Reasoning. Morgan Kaufmann, 1987.
M. Ginsberg. Multivalued logics: A uniform approach to inference in artificial intelligence. Computer Intelligence, 4:265–316, 1988.
S. Gottwald. A Treatise on Many-Valued Logics. Research Studies Press, 2001.
W. S. Hatcher. The Logical Foundations of Mathematics. Pergamon Press, 1982.
G. E. Hughes and M. J. Cresswell. An Introduction to Modal Logic. Methuen, 1968.
D. A. MacKenzie. Mechanizing Proof. MIT Press, 2001.
E. Mendelson. Introduction to Mathematical Logic. Chapman, 4th edition, 1997.
R. Muskens. Meaning and Partiality. CSLI Publications, 1995.
J. Villadsen. Combinators for paraconsistent attitudes. In P. de Groote et al., editors, Logical Aspects of Computational Linguistics, pages 261–278. Springer, 2001. LNCS 2099.
J. Villadsen. Paraconsistent knowledge bases and many-valued logic. In H.-M. Haav et al. (editors), International Baltic Conference on Databases and Information Systems, Volume 2, pages 77–90, Tallinn, Estonia, 2002.
J. Villadsen. A paraconsistent higher order logic. In Decker et al. [9], pages 33–49. Updated PCL 2002 paper available at CoRR (Computing Research Repository) http://www.arXiv.org/abs/cs.LO/0207088
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Villadsen, J. (2002). Paraconsistent Query Answering Systems. In: Carbonell, J.G., Siekmann, J., Andreasen, T., Christiansen, H., Motro, A., Legind Larsen, H. (eds) Flexible Query Answering Systems. FQAS 2002. Lecture Notes in Computer Science(), vol 2522. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36109-X_29
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DOI: https://doi.org/10.1007/3-540-36109-X_29
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