In this paper we present a new method of semantic schema integration, based on uncertain semantic mappings. The purpose of semantic schema integration is to produce a unified representation of multiple data sources. First, schema matching is performed to identify the semantic mappings between the schema objects. Then, an integrated schema is produced during the schema merging process based on the identified mappings. If all semantic mappings are known, schema merging can be performed (semi-)automatically

Magnani, M

McBrien, P

Montesi, D

Rizopoulos, N

Spiral - Imperial College Digital Repository

Uncertainty in Semantic Schema IntegrationNikos Rizopoulos1, Matteo Magnani2, Peter Mc.Brien1, and Danilo Montesi31 Department of Computing, Imperial College London{nr600,pjm}@doc.ic.ac.uk2 Department of Computer Science, University of Bolognamatteo.magnani@cs.unibo.it3 Department of Mathematics and Informatics, University of Camerinodanilo.montesi@unicam.it1 IntroductionIn this paper we present a new method of semantic schema integration, based onuncertain semantic mappings. The purpose of semantic schema integration is toproduce a unified representation of multiple data sources. First, schema matching[1] is performed to identify the semantic mappings between the schema objects.Then, an integrated schema is produced during the schema merging process [2]based on the identified mappings. If all semantic mappings are known, schemamerging can be performed (semi-)automatically.As an illustrative example, consider the schemas S1 and S2 in Figure 1.Schema S1 models a data source of undergraduate students. Undergraduates areregistered (reg) in courses that are taught (tch) by staff members. Schema S2models a data source of postgraduate students, which can also optionally registerin fourth-year courses to refresh their knowledge or familiarize themselves withnew subjects. Therefore, S1.student and S2.student are disjoint, while S1.coursesubsumes S2.course. Such semantic mappings drive the schema integration pro-cess. For example, the disjointness mapping between the student entities triggersschema transformations that rename the entities to make them distinct, e.g. intoug and pg, and add a union entity, e.g. student, that represents the union set ofboth undergraduate and postgraduate students.In this example, we already know the semantics of the schema objects, thus wecan specify their semantic mappings. However, this is not true in general. Manualschema matching is usually time consuming and automatic schema matching isuncertain because the semantics of schema objects cannot be directly compared.In order to take into account this uncertainty in the schema matching results,we extend the concept of semantic mapping.We assume to have a finite amount of belief, that can be distributed to al-ternative semantic mappings. When we are certain about a mapping, we assignall our belief to it. This is implicitly done by most existing schema matchingtechniques [1]. A straightforward extension of this concept can be obtained byallowing several alternative mappings to be possible, and distributing our beliefto them. For example, we may think that the two student entities in S1 and S2are either disjoint, in the case they refer to undergraduates and postgraduates,2S1 student reg1:N1:N course tch1:11:NstaffS2 student reg0:N0:N course tch1:10:NstaffFig. 1. Schema S1 and S2: undergraduate and postgraduate data sourcesor equivalent. This legitimate uncertainty should not prevent the integration ofthe schemas. In fact, we can think of two possible integrations, the former cor-responding to disjointness and the latter to equivalence. The uncertainty in themapping between the two student entities propagates in the corresponding alter-native integrated schemas. The final integrated schema is created by combiningall the produced mappings.2 A New Schema Integration Approach2.1 Uncertain Semantic RelationshipsAs already discussed in the introduction, for every pair of schema objects weconsider several alternative mappings, and our beliefs are distributed over them.The possible mappings are: equivalence ( S=), subset-subsumption (S⊂), superset-subsumption (S⊃), intersection (S∩), disjointness (S∩/), and incompatibility (S/∼) [3].We use Θ to refer to the set of all possible mappings. To represent beliefs, wehave adopted Shafer’s belief functions [4]. This choice is justified by the factthat Shafer’s belief functions can represent the main kinds of uncertainty thatare present in schema integration. An uncertain semantic relationship (USR)is defined by a special function m, that assigns a probability mass to sets ofsemantic mappings between schema objects. We omit the mathematical details,which can be found in [4].As in [3], the comparison of schema objects is performed by a pool of ex-perts, each one specialized on some features. However, to support the inherentuncertainty of schema matching, experts produce USRs. The mapping betweenany two schema objects is computed by aggregating the results of all the avail-able experts. The aggregation of USRs is easily achieved by using Dempster’scombination rule [4].As an example, consider the comparison of the two student entities in schemasS1 and S2, by means of three experts. The USR produced by one expert mightbe: m1({S∩, S⊃,S∩/,S/∼}) = 1. Another expert might produce the following USR:m2({ S=}) = .7,m2({ S⊂, S⊃,S∩/, S∩}) = .2,m2({Θ}) = .1. Finally, the third expert’soutput could be: m3({S∩,S∩/}) = .8,m3({Θ}) = .2. Due to space limitations, wecannot provide additional details about the experts. The combination of m1,m2,3and m3 is obtained by applying Dempster’s rule, and produces the followingUSR: m({S∩, S∩/}) = 4/5, m({S∩, S⊃, S∩/}) = 2/15, m({S∩, S⊃, S∩/, S/∼}) = 1/15 .2.2 Schema MergingIn the previous example we compared student entities, obtaining a set of possiblesemantic relationships between them, with a corresponding representation of ourbelief distribution. Similarly, we can compare the reg ER relationships, and allthe other objects.# S1.stud.,S2.stud. S1.reg,S2.reg S1.course,S2.course S1.staff,S2.staff S1.tch,S2.tch(a)S∩/S∩/S⊃ S=S⊃(b)S∩/S/∼S⊃ S=S⊃(c)S∩S∩/S⊃ S=S⊃(d)S∩ S∩S⊃ S=S⊃(e)S∩S⊃S⊃ S=S⊃(f)S∩S/∼S⊃ S=S⊃(g)S⊃S∩/S⊃ S=S⊃(h)S⊃ S∩S⊃ S=S⊃(i)S⊃S⊃S⊃ S=S⊃(j)S⊃S/∼S⊃ S=S⊃(k)S/∼S/∼S⊃ S=S⊃Table 1. Possible combinations of semantic relationships in the integrated schemaNow assume that the comparison of S1.reg and S2.reg provides the sameUSR as in the comparison of the student entities. Also, assume that S1.courseS⊃ S2.course, S1.tchS⊃ S2.tch, and S1.staffS= S2.staff are certain. We can build atable (Table 1), representing all possible combinations of semantic relationshipsbetween all pairs of schema objects.Notice that not all combinations are possible: the intersection relationshipbetween the two reg ER relationships specifies that there is at least one com-mon instance between S1.reg and S2.reg, i.e. there is a common instance ofS1.student and S2.student that is associated with a common instance of S1.courseand S2.course. Therefore, whenever student entities are disjoint (do not have anyinstances in common) reg ER relationships cannot be intersecting. Thus onlyeleven of the sixteen possible integrated schemas are considered in Table 1.Each row of this table corresponds to a possible integrated schema, whereeach semantic relationship defines a partial integrated schema. For example, inthe possible integrated schema (a) of Table 1 student entities are disjoint, whilein the possible integrated schema (c) S1.student intersects S2.student. The schemacorresponding to row (a) of Table 1 is illustrated in Figure 2.4S2.student S1.studentstudent6S1.reg1:N1:NS1.courseS2.course6S1.tch1:11:NS2.tch1:10:NstaffS2.reg0:N0:Nreg0:N0:NFig. 2. One of the final alternative integrated schemas generated by our approach,corresponding to row (a) of Table 1The belief distribution obtained as a combination of the aforementionedUSRs is defined by4: m{(a), (c), (d)} = 1625 , m{(a), (c)–(e)} = 875 , m{(a)–(f)} = 475 , m{(a), (c), (d), (g), (h)} = 1675 , m{(a), (c)–(e), (g)–(i)} = 4225 ,m{(a)–(j)} = 2225 , m{(a), (c), (d), (g), (h), (k)} = 475 , m{(a), (c)–(e), (g)–(i), (k)} = 2225 , m{(a)–(k)} = 1225 . The set {(a)–(k)}, together with the beliefdistribution m, is called an uncertain integrated schema, and is the final prod-uct of our schema integration approach on our working example. To reduce thecardinality of the possible integrated schemas, we can decide to keep only therows to whom an amount of probability mass over a given threshold is assigned.For example, we could dispose of all rows of Table 1 but (a), (c), and (d).3 ConclusionIn this paper we have presented a new method of semantic schema integration.Our approach differs from existing methods in that it handles the inherent uncer-tainty in (semi-)automatic schema matching, and supports six kinds of semanticrelationships between schema objects. These features are essential to cope withreal schema integration tasks, where many semantic relationships are possible,and it is very unlikely to know all of them with certainty.References1. Rahm, E., Bernstein, P.: A survey of approaches to automatic schema matching.VLDB Journal 10 (2001) 334–3502. Bernstein, P.: Applying model management to classical meta data problems. In:Proc. CIDR, 2003. (2003) 209–2203. Rizopoulos, N.: Automatic discovery of semantic relationships between schemaelements. In: ICEIS (1). (2004) 3–84. Shafer, G.: A mathematical theory of evidence. Princeton University Press (1976)4 With (b)–(d) we indicate all the rows between (b) and (d), i.e. (b), (c), (d).

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Uncertainty in Semantic Schema Integration

N. Rizopoulos

P. McBrien

MAGNANI, MATTEO

MONTESI, DANILO

Archivio istituzionale della ricerca - Alma Mater Studiorum Università di Bologna

Uncertainty in semantic schema integration

Uncertainty in Semantic Schema Integration

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