Abstract
Feature-based description logics replace the notion of roles, interpreted as binary relations, with features, interpreted as unary functions. Another notable feature of these logics is their use of path functional dependencies that allow for complex identification constraints to be formulated. The use of features and path functional dependencies makes the logics particularly well suited for capturing and integrating data sources conforming to an underlying object-relational schema that include a variety of common integrity constraints. We first survey expressive variants of feature logics, including the boundaries of decidability. We then survey a restricted tractable family of feature logics suited to query answering, and study the limits of tractability of reasoning.
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Notes
- 1.
Allowing the use of conjunction at the top level on the right-hand-side is a simple syntactic sugar.
- 2.
Unlike DL-Lite\(^\mathcal{(HF)}_{\mathrm {core}}\), that restricts the applicability of functional constraints in the presence of role hierarchies, we review what forms of role hierarchies can be captured while retaining the ability to specify arbitrary keys and functional dependencies.
References
Ackermann, W.: Uber die Erfullbarkeit gewisser Zahlausdrucke. Math. Ann. 100, 638–649 (1928)
Artale, A., Calvanese, D., Kontchakov, R., Zakharyaschev, M.: The DL-lite family and relations. J. Artif. Intell. Res. 36, 1–69 (2009). https://doi.org/10.1613/jair.282
Baader, F., Brandt, S., Lutz, C.: Pushing the EL envelope. In: Kaelbling, L.P., Saffiotti, A. (eds.) Proceedings of the Nineteenth International Joint Conference on Artificial Intelligence, IJCAI 2005, Edinburgh, Scotland, UK, 30 July–5 August 2005, pp. 364–369. Professional Book Center (2005). http://ijcai.org/Proceedings/05/Papers/0372.pdf
Berger, R.: The undecidability of the dominoe problem. Mem. Amer. Math. Soc. 66, 1–72 (1966)
van Emde Boas, P.: The convenience of tilings. In: Complexity, Logic, and Recursion Theory. pp. 331–363. Marcel Dekker Inc. (1997)
Borgida, A., Toman, D., Weddell, G.: On referring expressions in information systems derived from conceptual modelling. In: Comyn-Wattiau, I., Tanaka, K., Song, I.-Y., Yamamoto, S., Saeki, M. (eds.) ER 2016. LNCS, vol. 9974, pp. 183–197. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-46397-1_14
Borgida, A., Toman, D., Weddell, G.E.: On referring expressions in query answering over first order knowledge bases. In: Baral, C., Delgrande, J.P., Wolter, F. (eds.) Proceedings of the Fifteenth International Conference, Principles of Knowledge Representation and Reasoning KR 2016, Cape Town, South Africa, 25–29 April 2016, pp. 319–328. AAAI Press (2016). http://www.aaai.org/ocs/index.php/KR/KR16/paper/view/12860
Borgida, A., Weddell, G.: Adding uniqueness constraints to description logics. In: Bry, F., Ramakrishnan, R., Ramamohanarao, K. (eds.) DOOD 1997. LNCS, vol. 1341, pp. 85–102. Springer, Heidelberg (1997). https://doi.org/10.1007/3-540-63792-3_10
Brewka, G., Lang, J. (eds.): Principles of knowledge representation and reasoning. In: Proceedings of the Eleventh International Conference, KR 2008, Sydney, Australia, 16–19 September 2008. AAAI Press (2008)
Calvanese, D., De Giacomo, G., Lembo, D., Lenzerini, M., Rosati, R.: Tractable reasoning and efficient query answering in description logics: the DL-Lite family. J. Autom. Reasoning 39(3), 385–429 (2007). https://doi.org/10.1007/s10817-007-9078-x
Calvanese, D., De Giacomo, G., Lembo, D., Lenzerini, M., Rosati, R.: Path-based identification constraints in description logics. In: Brewka and Lang [9], pp. 231–241. http://www.aaai.org/Library/KR/2008/kr08-023.php
Calvanese, D., De Giacomo, G., Lembo, D., Lenzerini, M., Rosati, R.: Data complexity of query answering in description logics. Artif. Intell. 195, 335–360 (2013). https://doi.org/10.1016/j.artint.2012.10.003
Calvanese, D., De Giacomo, G., Lenzerini, M.: On the decidability of query containment under constraints. In: Mendelzon, A.O., Paredaens, J. (eds.) Proceedings of the Seventeenth ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems, 1–3 June 1998, Seattle, Washington, USA. pp. 149–158. ACM Press (1998). https://doi.org/10.1145/275487.275504
Calvanese, D., De Giacomo, G., Lenzerini, M.: Identification constraints and functional dependencies in description logics. In: Nebel, B. (ed.) Proceedings of the Seventeenth International Joint Conference on Artificial Intelligence, IJCAI 2001, Seattle, Washington, USA, 4–10 August 2001. pp. 155–160. Morgan Kaufmann (2001). http://ijcai.org/proceedings/2001-1
Chomicki, J., Imielinski, T.: Finite representation of infinite query answers. ACM Trans. Database Syst. 18(2), 181–223 (1993). https://doi.org/10.1145/151634.151635
Fürer, M.: Alternation and the ackermann case of the decision problem. L’Enseignement Math. 27, 137–162 (1981)
Jacques, J.S., Toman, D., Weddell, G.E.: Object-relational queries over cfdi\({}_{\text{nc}}\) knowledge bases: OBDA for the SQL-Literate. In: Kambhampati, S. (ed.) Proceedings of the Twenty-Fifth International Joint Conference on Artificial Intelligence, IJCAI 2016, New York, NY, USA, 9–15 July 2016, pp. 1258–1264. IJCAI/AAAI Press (2016). http://www.ijcai.org/Abstract/16/182
Jacques, J.S., Toman, D., Weddell, G.E.: Object-relational queries over cfdi\(\_\)nc knowledge bases: OBDA for the SQL-Literate (extended abstract). In: Lenzerini, M., Peñaloza, R. (eds.) Proceedings of the 29th International Workshop on Description Logics, Cape Town, South Africa, 22–25 April 2016. CEUR Workshop Proceedings, vol. 1577. CEUR-WS.org (2016). http://ceur-ws.org/Vol-1577/paper_10.pdf
Karp, R.M.: Reducibility among combinatorial problems. In: Miller, R.E., Thatcher, J.W., Bohlinger, J.D. (eds.) Complexity of Computer Computations. The IBM Research Symposia Series, pp. 85–103. Springer, Boston (1972). https://doi.org/10.1007/978-1-4684-2001-2_9
Khizder, V.L., Toman, D., Weddell, G.: Reasoning about duplicate elimination with description logic. In: Lloyd, J., et al. (eds.) CL 2000. LNCS (LNAI), vol. 1861, pp. 1017–1032. Springer, Heidelberg (2000). https://doi.org/10.1007/3-540-44957-4_68
Khizder, V.L., Toman, D., Weddell, G.E.: Adding aboxes to a description logic with uniqueness constraints via path agreements. In: Calvanese, D., et al. (eds.) Proceedings of the 2007 International Workshop on Description Logics (DL2007), Brixen-Bressanone, near Bozen-Bolzano, Italy, 8–10 June 2007. CEUR Workshop Proceedings, vol. 250. CEUR-WS.org (2007). http://ceur-ws.org/Vol-250/paper_69.pdf
Kontchakov, R., Lutz, C., Toman, D., Wolter, F., Zakharyaschev, M.: The combined approach to query answering in DL-Lite. In: Lin, F., Sattler, U., Truszczynski, M. (eds.) Proceedings of the Twelfth International Conference Principles of Knowledge Representation and Reasoning, KR 2010, Toronto, Ontario, Canada, 9–13 May 2010. AAAI Press (2010). http://aaai.org/ocs/index.php/KR/KR2010/paper/view/1282
Liu, L., Özsu, M.T. (eds.): Encyclopedia of Database Systems. Springer, US (2009). https://doi.org/10.1007/978-0-387-39940-9
Machtey, M., Young, P.: An Introduction to the General Theory of Algorithms. North-Holland, Amsterdam (1978)
McIntyre, S., Borgida, A., Toman, D., Weddell, G.E.: On limited conjunctions in polynomial feature logics, with applications in OBDA. In: Thielscher, M., Toni, F., Wolter, F. (eds.) Proceedings of the Sixteenth International Conference Principles of Knowledge Representation and Reasoning, KR 2018, Tempe, Arizona, 30 October–2 November 2018, pp. 655–656. AAAI Press (2018). https://aaai.org/ocs/index.php/KR/KR18/paper/view/18016
McIntyre, S., Borgida, A., Toman, D., Weddell, G.E.: On limited conjunctions and partial features in parameter tractable feature logics. In: Proceedings of the Thirty-Third AAAI Conference on Artificial Intelligence, 27 January–1 February 2019, Honolulu, Hawaii, U.S.A. (2019, in press)
Song, I., Chen, P.P.: Entity relationship model. In: Liu and Özsu [23], pp. 1003–1009. https://doi.org/10.1007/978-0-387-39940-9_148
Thalheim, B.: Extended entity-relationship model. In: Liu and Özsu [23], pp. 1083–1091. https://doi.org/10.1007/978-0-387-39940-9_157
Toman, D., Weddell, G.E.: On attributes, roles, and dependencies in description logics and the ackermann case of the decision problem. In: Goble, C.A., McGuinness, D.L., Möller, R., Patel-Schneider, P.F. (eds.) Proceedings of the Working Notes of the 2001 International Description Logics Workshop (DL-2001), Stanford, CA, USA, 1–3 August 2001. CEUR Workshop Proceedings, vol. 49. CEUR-WS.org (2001). http://ceur-ws.org/Vol-49/TomanWeddell-76start.ps
Toman, D., Weddell, G.E.: On reasoning about structural equality in XML: a description logic approach. Theor. Comput. Sci. 336(1), 181–203 (2005). https://doi.org/10.1016/j.tcs.2004.10.036
Toman, D., Weddell, G.E.: On the interaction between inverse features and path-functional dependencies in description logics. In: Kaelbling, L.P., Saffiotti, A. (eds.) Proceedings of the Nineteenth International Joint Conference on Artificial Intelligence, IJCAI 2005, Edinburgh, Scotland, UK, 30 July–5 August 2005, pp. 603–608. Professional Book Center (2005). http://ijcai.org/Proceedings/05/Papers/1421.pdf
Toman, D., Weddell, G.: On keys and functional dependencies as first-class citizens in description logics. In: Furbach, U., Shankar, N. (eds.) IJCAR 2006. LNCS (LNAI), vol. 4130, pp. 647–661. Springer, Heidelberg (2006). https://doi.org/10.1007/11814771_52
Toman, D., Weddell, G.: On order dependencies for the semantic web. In: Parent, C., Schewe, K.-D., Storey, V.C., Thalheim, B. (eds.) ER 2007. LNCS, vol. 4801, pp. 293–306. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-75563-0_21
Toman, D., Weddell, G.E.: Identifying objects over time with description logics. In: Brewka and Lang [9], pp. 724–732. http://www.aaai.org/Library/KR/2008/kr08-071.php
Toman, D., Weddell, G.E.: On keys and functional dependencies as first-class citizens in description logics. J. Autom. Reasoning 40(2–3), 117–132 (2008). https://doi.org/10.1007/s10817-007-9092-z
Toman, D., Weddell, G.E.: Applications and extensions of PTIME description logics with functional constraints. In: Boutilier, C. (ed.) Proceedings of the 21st International Joint Conference on Artificial Intelligence, IJCAI 2009, Pasadena, California, USA, 11–17 July 2009, pp. 948–954 (2009). http://ijcai.org/Proceedings/09/Papers/161.pdf
Toman, D., Weddell, G.: Conjunctive query answering in \({\cal{CFD}}_{nc}\): a PTIME description logic with functional constraints and disjointness. In: Cranefield, S., Nayak, A. (eds.) AI 2013. LNCS (LNAI), vol. 8272, pp. 350–361. Springer, Cham (2013). https://doi.org/10.1007/978-3-319-03680-9_36
Toman, D., Weddell, G.: On adding inverse features to the description logic \(\cal{CFD}^{\forall }_{nc}\). In: Pham, D.-N., Park, S.-B. (eds.) PRICAI 2014. LNCS (LNAI), vol. 8862, pp. 587–599. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-13560-1_47
Toman, D., Weddell, G.: On the krom extension of \(\cal{CFDI}^{\forall -}_{nc}\). In: Pfahringer, B., Renz, J. (eds.) AI 2015. LNCS (LNAI), vol. 9457, pp. 559–571. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-26350-2_50
Toman, D., Weddell, G.: On partial features in the \(\cal{DLF}\) Family of Description Logics. In: Booth, R., Zhang, M.-L. (eds.) PRICAI 2016. LNCS (LNAI), vol. 9810, pp. 529–542. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-42911-3_44
Toman, D., Weddell, G.E.: On partial features in the DLF dialects of description logic with inverse features. In: Artale, A., Glimm, B., Kontchakov, R. (eds.) Proceedings of the 30th International Workshop on Description Logics, Montpellier, France, 18–21 July 2017. CEUR Workshop Proceedings, vol. 1879. CEUR-WS.org (2017). http://ceur-ws.org/Vol-1879/paper44.pdf
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McIntyre, S., Toman, D., Weddell, G. (2019). FunDL. In: Lutz, C., Sattler, U., Tinelli, C., Turhan, AY., Wolter, F. (eds) Description Logic, Theory Combination, and All That. Lecture Notes in Computer Science(), vol 11560. Springer, Cham. https://doi.org/10.1007/978-3-030-22102-7_19
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