Abstract
We investigate whether identification constraints such as keys and functional dependencies can be granted full status as concept constructors in a Boolean-complete description logic. In particular, we show that surprisingly simple forms of such constraints lead to undecidability of the associated logical implication problem if they are allowed within the scope of a negation or on the left-hand side of inclusion dependencies. We then show that allowing a very general form of identification constraint to occur in the scope of monotone concept constructors on the right-hand side of inclusion dependencies still leads to decidable implication problems. We consider the relationship between certain classes of identification constraints and nominals.
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Berger, R.: The undecidability of the domino problem. Mem. Am. Math. Soc. 66, 1–72 (1966)
Biskup, J., Polle, T.: Decomposition of database classes under path functional dependencies and onto constraints. In: Schewe, K.-D., Thalheim, B. (eds.) Foundations of Information and Knowledge Systems, pp. 31–49. Springer, New York (2000)
Biskup, J., Polle, T.: Adding inclusion dependencies to an object-oriented data model with uniqueness constraints. Acta Inform. 39, 391–449 (2003)
Borgida, A., Weddell, G.E.: Adding uniqueness constraints to description logics (preliminary report). In: International Conference on Deductive and Object-Oriented Databases, pp. 85–102, Montreux, 8–12 December 1997
Calvanese, D., De Giacomo, G., Lenzerini, M.: Identification constraints and functional dependencies in description logics. In: Proc. of the 17th Int. Joint Conf. on Artificial Intelligence (IJCAI), pp. 155–160, Seattle, 4–10 August 2001
Calvanese, D., De Giacomo, G., Lenzerini, M.: Representing and reasoning on XML documents: a description logic approach. J. Log. Comput. 9(3), 295–318 (1999)
Calvanese, D., Lenzerini, M., De Giacomo, G.: Keys for free in description logics. In: Proc. of the 2000 Int. Workshop on Description Logics, pp. 79–88, Aachen, 17–19 August 2000
DeHaan, D., Toman, D., Weddell, G.E.: Rewriting aggregate queries using description logics. In: Description Logics 2003, vol. 81, pp. 103–112. CEUR-WS, Aachen (2003)
Ito, M., Weddell, G.E.: Implication problems for functional constraints on databases supporting complex objects. J. Comput. Syst. Sci. 49(3), 726–768 (1994)
Khizder, V.L., Toman, D., Weddell, G.E.: Reasoning about duplicate elimination with description logic. In: Rules and Objects in Databases (DOOD, Part of CL’00), pp. 1017–1032, London, 24–28 July 2000
Khizder, V.L., Toman, D., Weddell, G.E.: On decidability and complexity of description logics with uniqueness constraints. In: Int. Conf. on Database Theory ICDT’01, pp. 54–67, London, 4–6 January 2001
Liu, H., Toman, D., Weddell, G.E.: Fine grained information integration with description logic. In: Description Logics 2002, vol. 53, pp. 1–12. CEUR-WS, Aachen (2002)
Lutz, C., Milicic, M.: Description logics with concrete domains and functional dependencies. In: Proc. Eur. Conf. on Artificial Intelligence (ECAI), pp. 378–382, Valencia, 23–27 August 2004
Lutz, C., Areces, C., Horrocks, I., Sattler, U.: Keys, nominals, and concrete domains. In: Proc. of the 18th Int. Joint Conf. on Artificial Intelligence (IJCAI), pp. 349–354. Morgan Kaufmann, San Mateo (2003)
Sattler, U., Calvanese, D., Molitor, R.: Relationships with other formalisms. In: The Description Logic Handbook: Theory, Implementation, and Applications, chapter 4, pp. 137–177. Cambridge University Press, Cambridge (2003)
Stanchev, L., Weddell, G.E.: Index selection for embedded control applications using description logics. In: Description Logics 2003, vol. 81, pp. 9–18. CEUR-WS, Aachen (2003)
Toman, D., Weddell, G.: On reasoning about structural equality in XML: a description logic approach. Theor. Comput. Sci. 336(1), 181–203 (2005)
Toman, D., Weddell G.: On the interaction between inverse features and path-functional dependencies in description logics. In: Proc. of the 19th Int. Joint Conf. on Artificial Intelligence (IJCAI), pp. 603–608. Morgan Kaufmann, San Mateo (2005)
Toman, D., Weddell, G.E.: On attributes, roles, and dependencies in description logics and the Ackermann case of the decision problem. In: Description Logics, vol. 49, pp. 76–85. CEUR-WS, Aachen (2001)
Toman, D., Weddell, G.E.: Attribute inversion in description logics with path functional dependencies. In: Description Logics 2004, vol. 104, pp. 178–187. CEUR-WS, Aachen (2004)
Toman, D., Weddell, G.E.: On path-functional dependencies as first-class citizens in description logics. In: Description Logics, vol. 1475. CEUR-WS, Aachen (2005)
van Emde Boas, P.: The convenience of tilings. In: Complexity, Logic, and Recursion Theory. Lecture Notes in Pure and Applied Mathematics, vol. 187, pp. 331–363. Marcel Dekker, New York (1997)
Weddell, G.: A theory of functional dependencies for object oriented data models. In: Int. Conf. on Deductive and Object-Oriented Databases, pp. 165–184, Kyoto, 4–6 December 1989
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Toman, D., Weddell, G. On Keys and Functional Dependencies as First-Class Citizens in Description Logics. J Autom Reasoning 40, 117–132 (2008). https://doi.org/10.1007/s10817-007-9092-z
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DOI: https://doi.org/10.1007/s10817-007-9092-z