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Conjunctive Query Answering with OWL 2 QL

Profile image of S. KikotS. Kikot

2012

Abstract

We present a novel rewriting technique for conjunctive query answering over OWL 2 QL ontologies. In general, the obtained rewritings are not necessarily correct and can be of exponential size in the length of the query. We argue, however, that in most, if not all, practical cases the rewritings are correct and of polynomial size. Moreover, we prove some sufficient conditions, imposed on queries and ontologies, that guarantee correctness and succinctness. We also support our claim by experimental results. m j=1 D j over propositional variables p 1 , . . . , p n as an OWL 2 QL TBox,

Figures (11)
Example 3 Let 7 = {AC 4S-.B,BCAS.A’, A’ CAT} and q(x) = {S(y, x), S(y, z), T(z, v)}. The answer vari- able x must be mapped by a to an ABox element. However, y can be mapped either to an ABox element or to the point a(a) - wig-p] provided that a(a) is an instance of A (and so of 4S~.B). In the latter case, we have two possibilities for mapping z: either to a(x) -wjg- )-Wys.a‘), in which case we must further set a(v) = a(x) - wis- B] - Wig.) * Wert}, OF to a(x), provided that a(x) is an instance of AT. In the picture below, these two (partial) maps are denoted by f and g. The observations made in Example 3 are formalised in our central definition. Given a pair (t, t’) of adjacent terms in (the graph of) q, we define a tree witness for (t, t') to be
Example 3 Let 7 = {AC 4S-.B,BCAS.A’, A’ CAT} and q(x) = {S(y, x), S(y, z), T(z, v)}. The answer vari- able x must be mapped by a to an ABox element. However, y can be mapped either to an ABox element or to the point a(a) - wig-p] provided that a(a) is an instance of A (and so of 4S~.B). In the latter case, we have two possibilities for mapping z: either to a(x) -wjg- )-Wys.a‘), in which case we must further set a(v) = a(x) - wis- B] - Wig.) * Wert}, OF to a(x), provided that a(x) is an instance of AT. In the picture below, these two (partial) maps are denoted by f and g. The observations made in Example 3 are formalised in our central definition. Given a pair (t, t’) of adjacent terms in (the graph of) q, we define a tree witness for (t, t') to be
We obviously have a tree witness f for (#1, y2) such that dom f = {x1, y2,ys} and f—'(rp) = {1, yz}, and also a tree witness g for (a4, y3) with domg = {24, y3, y2} and g (rf) = {x4,y2}. Although these tree witnesses cover the whole query q, they are only ‘realised’ in Cx under con- flicting maps: f sends x1, y3 to a and yp to a- wrt}, while g sends £4, yz to a and y3 to a- wiR-7); in fact, K FF q(a, a).
We obviously have a tree witness f for (#1, y2) such that dom f = {x1, y2,ys} and f—'(rp) = {1, yz}, and also a tree witness g for (a4, y3) with domg = {24, y3, y2} and g (rf) = {x4,y2}. Although these tree witnesses cover the whole query q, they are only ‘realised’ in Cx under con- flicting maps: f sends x1, y3 to a and yp to a- wrt}, while g sends £4, yz to a and y3 to a- wiR-7); in fact, K FF q(a, a).
To illustrate, consider the CQ q(yo) for n = m = 2 and sup- pose that y is such that the P~ X}-subtree of Cz, contains the fragment as shown in the picture below. We can construct a tree witness f for (z{, 2) by taking f(zt) =o. f(z4) = 11, f(y2) = 72, after which we have three different options for defining f(z?) and f(z@): go back to ro, go to ry and then take the C2-branch, or take the C'- branch starting from r2. The last two tree witnesses give the same tree witness formula, which is different from that given by the first tree witness. Imagine now some large n and m. It is this fact that makes it ‘hard’ to construct a rewriting for a(yo) and Ty.
To illustrate, consider the CQ q(yo) for n = m = 2 and sup- pose that y is such that the P~ X}-subtree of Cz, contains the fragment as shown in the picture below. We can construct a tree witness f for (z{, 2) by taking f(zt) =o. f(z4) = 11, f(y2) = 72, after which we have three different options for defining f(z?) and f(z@): go back to ro, go to ry and then take the C2-branch, or take the C'- branch starting from r2. The last two tree witnesses give the same tree witness formula, which is different from that given by the first tree witness. Imagine now some large n and m. It is this fact that makes it ‘hard’ to construct a rewriting for a(yo) and Ty.
A good illuminative example of a CQ with exponentially many tree witness formulas is q(yo) over the TBox 7, con- structed above for a CNF x. One can show that the pairs (z}, z]_,) give rise to exponentially many different tree wit- ness formulas tw for a suitable y.
A good illuminative example of a CQ with exponentially many tree witness formulas is q(yo) over the TBox 7, con- structed above for a CNF x. One can show that the pairs (z}, z]_,) give rise to exponentially many different tree wit- ness formulas tw for a suitable y.
Sufficient Conditions for Polynomial Rewriting The rewriting q,. is exponentially long if there are exponen- tially many tree witness formulas tw; for some pair (t, t’) of adjacent terms in q. Each tw; is determined subtree of C7 (containing the range of /), the domain dom f of f and the set f~'(ry); the terms in this set will be called the roots of f. Now we show that, for a large c q and by the RB- ass of CQs OWL 2 QL TBoxes 7, all tree witnesses for the same pair (¢, t’) in q have the same domain and roots. As the num- ber o of T, over, in |q demo and t f distinct RB-subtrees of C7 is polynomia in the size the rewriting q, in this case is also polynomial; more- we show that it can be constructed in polynomial time and |7|. Roughly, Theorem 19 to be proved below nstrates that this can be done if condition (conf) holds here are no roles TJ’, S' and a tree witness f for which f(q) and C7 simultaneously contain fragments of the form
Sufficient Conditions for Polynomial Rewriting The rewriting q,. is exponentially long if there are exponen- tially many tree witness formulas tw; for some pair (t, t’) of adjacent terms in q. Each tw; is determined subtree of C7 (containing the range of /), the domain dom f of f and the set f~'(ry); the terms in this set will be called the roots of f. Now we show that, for a large c q and by the RB- ass of CQs OWL 2 QL TBoxes 7, all tree witnesses for the same pair (¢, t’) in q have the same domain and roots. As the num- ber o of T, over, in |q demo and t f distinct RB-subtrees of C7 is polynomia in the size the rewriting q, in this case is also polynomial; more- we show that it can be constructed in polynomial time and |7|. Roughly, Theorem 19 to be proved below nstrates that this can be done if condition (conf) holds here are no roles TJ’, S' and a tree witness f for which f(q) and C7 simultaneously contain fragments of the form
Here, by f(q) we mean the quotient q;/~ of q; modulo the equivalence relation ~ defined by taking s ~ s’ iff f(s) = f(s’). Roles T and S are called adjacent in f(q) if T(s1, 52), S(s2,53) € f(q), for some s; € term f(q) such that 82 ¢ f~'(rr). ie of: = << 2 ‘eee we _
Here, by f(q) we mean the quotient q;/~ of q; modulo the equivalence relation ~ defined by taking s ~ s’ iff f(s) = f(s’). Roles T and S are called adjacent in f(q) if T(s1, 52), S(s2,53) € f(q), for some s; € term f(q) such that 82 ¢ f~'(rr). ie of: = << 2 ‘eee we _
It turns out that if all tree witnesses f for a pair of terms in q are perfect then all of them have the same domain and roots, and so (i) the tree-witness formulas twy occur in the disjunctions for the same edges (t, t’) and (ii) the twy may differ only in their extar p(t) conjuncts. In the following example, exponentially many different tree witnesses give rise to the same tree witness formula. Example 14 Consider 7, = {A C AT, T C S7} and a(x) = {T (x,y), S(y, z)}. We have C7, — inv(T,S') and C7, —& inv(R, R-), for every role R. Both T and S~ are forward roles in 7;. The homomorphism f shown below is a perfect tree witness for (x, y):
It turns out that if all tree witnesses f for a pair of terms in q are perfect then all of them have the same domain and roots, and so (i) the tree-witness formulas twy occur in the disjunctions for the same edges (t, t’) and (ii) the twy may differ only in their extar p(t) conjuncts. In the following example, exponentially many different tree witnesses give rise to the same tree witness formula. Example 14 Consider 7, = {A C AT, T C S7} and a(x) = {T (x,y), S(y, z)}. We have C7, — inv(T,S') and C7, —& inv(R, R-), for every role R. Both T and S~ are forward roles in 7;. The homomorphism f shown below is a perfect tree witness for (x, y):
In the proof of Lemma 16, we construct a finite sequence f ; of tree-shaped CQs f; such that the final f,, is a univer- sal tree witness for (t, t’). We begin by taking all the atoms with terms ¢, t’ and then try to satisfy the tree witness condi- tion (t1) by adding atoms with new terms to the current f;,. Condition (perf), which is being checked during the con- struction, allows us to decide whether we have to add a new term to f; or reuse an existing one. To illustrate, we give one more example.
In the proof of Lemma 16, we construct a finite sequence f ; of tree-shaped CQs f; such that the final f,, is a univer- sal tree witness for (t, t’). We begin by taking all the atoms with terms ¢, t’ and then try to satisfy the tree witness condi- tion (t1) by adding atoms with new terms to the current f;,. Condition (perf), which is being checked during the con- struction, allows us to decide whether we have to add a new term to f; or reuse an existing one. To illustrate, we give one more example.
Example 18 Consider T = {A ECE 4S.C,C EC AT", AS” CAR, RCR, BCA TT CTATC s} and q(xo) = {S(xo,y1), R’(y1, y2), R(ys, yo), T (ya, ys) } in the picture above. A universal tree witness for (20, 41) must contain S(ao, y1). As the role in R’(y1, y2) is forward, the universal tree witness must contain this atom too. The role R in R~ (yz, y3) is also forward, so we add this atom and identify y; with y3. This gives three approximations of the universal tree witness we are constructing: In T (ya, ys), the role T is twisty in 7. The canonical model Cy suggests two alternative ways of treating T(y1, y3): ei- ther to add it as it is, or to identify y4 with root xo. Thus, no universal tree witness for (xo, y1) exists. This is also sig- nalled by the fact that condition (perf) fails: by identifying yi and y3, we make S and T adjacent, while both suc(S, T’) and inv(S, T) hold in C7. Note that S and T were not adja- cent in the original query q; that is why (perf) is checked for the image f(q) of every tree witness f. As the number of tree witnesses can be exponential, this complication might suggest that (perf) cannot be checked efficiently. The proof
Example 18 Consider T = {A ECE 4S.C,C EC AT", AS” CAR, RCR, BCA TT CTATC s} and q(xo) = {S(xo,y1), R’(y1, y2), R(ys, yo), T (ya, ys) } in the picture above. A universal tree witness for (20, 41) must contain S(ao, y1). As the role in R’(y1, y2) is forward, the universal tree witness must contain this atom too. The role R in R~ (yz, y3) is also forward, so we add this atom and identify y; with y3. This gives three approximations of the universal tree witness we are constructing: In T (ya, ys), the role T is twisty in 7. The canonical model Cy suggests two alternative ways of treating T(y1, y3): ei- ther to add it as it is, or to identify y4 with root xo. Thus, no universal tree witness for (xo, y1) exists. This is also sig- nalled by the fact that condition (perf) fails: by identifying yi and y3, we make S and T adjacent, while both suc(S, T’) and inv(S, T) hold in C7. Note that S and T were not adja- cent in the original query q; that is why (perf) is checked for the image f(q) of every tree witness f. As the number of tree witnesses can be exponential, this complication might suggest that (perf) cannot be checked efficiently. The proof
OWL 2 QL ontologies—Adolena (A), University (U) and Stockexchange (S)—using the same conjunctive queries as in (Pérez-Urbina, Motik, and Horrocks 2009; Rosati and Al- matelli 2010; Gottlob, Orsi, and Pieris 2011) and two new ones (Q6 and Q7); the ontologies and queries are available at www.dcs.bbk.ac.uk/~roman/query-rewriting. The results of the exneriments are collected in the table above.
OWL 2 QL ontologies—Adolena (A), University (U) and Stockexchange (S)—using the same conjunctive queries as in (Pérez-Urbina, Motik, and Horrocks 2009; Rosati and Al- matelli 2010; Gottlob, Orsi, and Pieris 2011) and two new ones (Q6 and Q7); the ontologies and queries are available at www.dcs.bbk.ac.uk/~roman/query-rewriting. The results of the exneriments are collected in the table above.
Proof We construct inductively a sequence of sets of terms Do g Di G-: G Dx, a sequence of tree subreducts f; of q over D; and homomorphisms a;: f:(q@) > gi(q) and Bi: filq) > hi(q) such that dom f, = dom g = dom h and the following diagram commutes: Here hp, and gp, are the restrictions of h and g onto D;, respectively. For each i, we denote the distance from h;(w) to the root h,(t) in hi (q) by ||h;(u)||, and similarly for g;(u) and f;(w). Recall that f; = f;(q) is a tree with root f;(t): we write u ~+5,(q) U to say that v is a child of u in this tree.
Proof We construct inductively a sequence of sets of terms Do g Di G-: G Dx, a sequence of tree subreducts f; of q over D; and homomorphisms a;: f:(q@) > gi(q) and Bi: filq) > hi(q) such that dom f, = dom g = dom h and the following diagram commutes: Here hp, and gp, are the restrictions of h and g onto D;, respectively. For each i, we denote the distance from h;(w) to the root h,(t) in hi (q) by ||h;(u)||, and similarly for g;(u) and f;(w). Recall that f; = f;(q) is a tree with root f;(t): we write u ~+5,(q) U to say that v is a child of u in this tree.

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References (19)

  1. Abiteboul, S.; Hull, R.; and Vianu, V. 1995. Foundations of Databases. Addison-Wesley.
  2. Baader, F.; Calvanese, D.; McGuinness, D.; Nardi, D.; and Patel-Schneider, P., eds. 2003. The Description Logic Hand- book: Theory, Implementation and Applications. Cambridge University Press.
  3. Baader, F.; Brandt, S.; and Lutz, C. 2005. Pushing the EL envelope. In Proc. of the 19th Int. Joint Conf. on Artificial Intelligence, IJCAI-05, 364-369. Professional Book Center.
  4. Baader, F.; Brandt, S.; and Lutz, C. 2008. Pushing the EL envelope further. In Clark, K., and Patel-Schneider, P. F., eds., Proc. of the OWLED 2008 DC Workshop on OWL: Ex- periences and Directions.
  5. Borodin, A.; von zur Gathen, J.; and Hopcroft, J. E. 1982. Fast parallel matrix and GCD computations. In Proc. of the 23rd Annual Symp. on Foundations of Computer Science, FOCS'82, 65-71. IEEE Computer Society.
  6. Calvanese, D.; De Giacomo, G.; Lembo, D.; Lenzerini, M.; and Rosati, R. 2007a. Tractable reasoning and efficient query answering in description logics: The DL-Lite family. J. of Automated Reasoning 39(3):385-429.
  7. Calvanese, D.; De Giacomo, G.; Lembo, D.; Lenzerini, M.; Poggi, A.; and Rosati, R. 2007b. Ontology-based database access. In Proc. of the 15th Ital. Conf. on Database Systems, SEBD 2007, 324-331.
  8. Chortaras, A.; Trivela, D.; and Stamou, G. 2011. Goal- oriented query rewriting for OWL 2 QL. In Proc. of the 24th Int. Workshop on Description Logics, DL 2011, vol. 745 of CEUR Workshop Proceedings. CEUR-WS.org. Gottlob, G., and Schwentick, T. 2011. Rewriting ontological queries into small nonrecursive datalog programs. In Proc. of the 24th Int. Workshop on Description Logics, DL 2011, vol. 745 of CEUR Workshop Proceedings. CEUR-WS.org. Gottlob, G.; Orsi, G.; and Pieris, A. 2011. Ontological queries: Rewriting and optimization. In Proc. of the the 27th Int. Conf. on Data Engineering, ICDE 2011, 2-13. IEEE Computer Society.
  9. Kikot, S.; Kontchakov, R.; and Zakharyaschev, M. 2011. On (In)Tractability of OBDA with OWL 2 QL. In Proc. of the 24th Int. Workshop on Description Logics, DL 2011, vol. 745 of CEUR Workshop Proceedings. CEUR-WS.org. Kikot, S.; Kontchakov, R.; Podolskii, V.; and Zakhary- aschev, M. 2012. Exponential lower bounds and separation for query rewriting. CoRR, arXiv:1202.4193, 2012.
  10. Kontchakov, R.; Lutz, C.; Toman, D.; Wolter, F.; and Za- kharyaschev, M. 2010. The combined approach to query answering in DL-Lite. In Proc. of the 12th Int. Conf. on Principles of Knowledge Representation and Reasoning, KR 2010. AAAI Press.
  11. Kontchakov, R.; Lutz, C.; Toman, D.; Wolter, F.; and Za- kharyaschev, M. 2011. The combined approach to ontology- based data access. In Proc. of the 20th Int. Joint Conf. on Ar- tificial Intelligence, IJCAI-2011, 2656-2661. AAAI Press.
  12. Lenzerini, M. 2002. Data integration: A theoretical perspec- tive. In Proc. of the 21st ACM SIGACT SIGMOD SIGART Symp. on Principles of Database Systems, PODS 2002, 233- 246. Lutz, C.; Toman, D.; and Wolter, F. 2009. Conjunctive query answering in the description logic EL using a rela- tional database system. In Proc. of the 21st Int. Joint Conf. on Artificial Intelligence, IJCAI 2009, 2070-2075. AAAI Press.
  13. Pérez-Urbina, H.; Motik, B.; and Horrocks, I. 2009. A comparison of query rewriting techniques for DL-Lite. In Int. Workshop on Description Logics, DL 2009, vol. 477 of CEUR Workshop Proceedings. CEUR-WS.org.
  14. Raz, R., and McKenzie, P. 1997. Separation of the monotone nc hierarchy. In Proc. of the 38th Annual Symp. on Founda- tions of Computer Science, FOCS'97, 234-243. IEEE Com- puter Society.
  15. Raz, R., and Wigderson, A. 1992. Monotone circuits for matching require linear depth. J. ACM 39(3):736-744.
  16. Razborov, A. 1985. Lower bounds for the monotone com- plexity of some Boolean functions. Dokl. Akad. Nauk SSSR 281(4):798-801.
  17. Rodriguez Muro, M., and Calvanese, D. 2011a. Depen- dencies to optimize ontology based data access. In Proc. of the 24th Int. Workshop on Description Logics, DL 2011, vol. 745 of CEUR Workshop Proceedings. CEUR-WS.org.
  18. Rodriguez Muro, M., and Calvanese, D. 2011b. Semantic index: Scalable query answering without forward chaining or exponential rewritings. In Proc. of the 10th Int. Semantic Web Conf., ISWC 2011.
  19. Rosati, R., and Almatelli, A. 2010. Improving query an- swering over DL-Lite ontologies. In Proc. of the 12th Int. Conf. on Principles of Knowledge Representation and Rea- soning, KR 2010. AAAI Press.

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OWL 2 QL is the profile of OWL 2 targeted to Ontology-Based Data Access (OBDA) scenarios, where large amount of data are to be accessed, and thus answering conjunctive queries over data is the main task. However, this task is quite restrained wrt the classical KR Ask-and-Tell framework based on querying the whole theory, not only facts (data). If we use SPARQL as query language, we get much closer to this ideal. Indeed, SPARQL queries over OWL 2 QL, under the so-called Direct Semantics Entailment Regime, may comprise any assertion expressible in the language, i.e., both ABox atoms and TBox atoms, including inequalities expressed by means of DifferentIndividuals. Nevertheless this regime is hampered by the assumption that variables in queries need to be typed, meaning that the same variable cannot occur in positions of different types, e.g., both in class and individual position (punning). In this paper we dismiss this limiting assumption by resorting to a recent meta modeling semantics and show that query answering in the resulting entailment regime is polynomially compilable into Datalog (and hence PTIME wrt both TBox and ABox).

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Answering over OWL Ontologies
Ilianna Kollia

2011

The SPARQL query language is currently being extended by W3C with so-called entailment regimes, which define how queries are evaluated under more expressive semantics than SPARQL’s standard simple entailment. We describe a sound and complete algorithm for the OWL Direct Semantics entailment regime. The queries of the regime are very expressive since variables can occur within complex class expressions and can also bind to class or property names. We propose several novel optimizations such as strategies for determining a good query execution order, query rewriting techniques, and show how specialized OWL reasoning tasks and the class and property hierarchy can be used to reduce the query execution time. We provide a prototypical implementation and evaluate the efficiency of the proposed optimizations. For standard conjunctive queries our system performs comparably to already deployed systems. For complex queries an improvement of up to three orders of magnitude can be observed.

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SUMA: A Partial Materialization-Based Scalable Query Answering in OWL 2 DL
qasim yasin

Data Science and Engineering, 2021

Ontology-mediated querying (OMQ) provides a paradigm for query answering according to which users not only query records at the database but also query implicit information inferred from ontology. A key challenge in OMQ is that the implicit information may be infinite, which cannot be stored at the database and queried by off -the -shelf query engine. The commonly adopted technique to deal with infinite entailments is query rewriting, which, however, comes at the cost of query rewriting at runtime. In this work, the partial materialization method is proposed to ensure that the extension is always finite. The partial materialization technology does not rewrite query but instead computes partial consequences entailed by ontology before the online query. Besides, a query analysis algorithm is designed to ensure the completeness of querying rooted and Boolean conjunctive queries over partial materialization. We also soundly and incompletely expand our method to support highly expressive...

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On the SPARQL Direct Semantics Entailment Regime for OWL 2 QL
Antonella Poggi

2016

OWL 2 QL is the profile of OWL 2 targeted to Ontology-Based Data Access (OBDA) scenarios, where large amount of data are to be accessed and thus query answering is required to be especially efficient in the size of such data, namely AC0 in data complexity. On the other hand, the syntax and the semantics of the SPARQL query language for OWL 2 is defined by means of the Direct Semantics Entailment Regime (DSER), which considers queries including any assertion expressible in the language of the queried ontology, i.e., both ABox atoms, TBox atoms and inequalities expressed by means of DifferentIndividuals atoms. Thus, in this paper, we investigate query answering over OWL 2 QL under DSER. In particular, we show that, by virtue of the restricted meaning assigned to existential variables and union, query answering can be reduced to the evaluation of a Datalog program. Finally, we investigate query answering under a new SPARQL entailment regime, called Direct Semantics Answering Regime (DS...

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