A Formal Approach for RDF/S Ontology Evolution George Konstantinidis and Giorgos Flouris and Grigoris Antoniou and Vassilis Christophides1 Abstract. In this paper, we consider the problem of ontology evo- the cases and options considered are exhaustive. lution in the face of a change operation. We devise a general-purpose To overcome these limitations, we propose an ontology evolution algorithm for determining the effects and side-effects of a requested framework and elaborate on its formal foundations. Our methodol- elementary or complex change operation. Our work is inspired by ogy is driven by ideas and principles of the belief revision literature belief revision principles (i.e., validity, success and minimal change) [3]. In particular, we adopt the Principle of Success (every change and allows us to handle any change operation in a provably ratio- operation is actually implemented) and the Principle of Validity (re- nal and consistent manner. To the best of our knowledge, this is the sulting ontology is valid, i.e., it satisfies all the validity constraints of first approach overcoming the limitations of existing solutions, which the underlying language). Satisfying both these requirements is not deal with each change operation on a per-case basis. Additionally, trivial, as the straightforward application of a change operation upon we rely on our general change handling algorithm to implement spe- an ontology can often lead to invalidity, in which case certain ad- cialized versions of it, one per desired change operation, in order to ditional actions (side-effects) should be executed to restore validity. compute the equivalent set of effects and side-effects.2 Sometimes, there may be more than one ways to do so, in which case a selection mechanism should be in place to determine the “best” op- tion. In this paper, we employ a technique inspired by the Principle of 1 INTRODUCTION Minimal Change [3] (stating that the appropriate result of changing Stored knowledge, in any knowledge-based application, may need an ontology should be as “close” as possible to the original). to change due to various reasons, including changes in the modeled The general idea of our approach is to first determine all the inva- world, new information on the domain, newly-gained access to infor- lidities that any given change (elementary or composite) could cause mation previously unknown, and other eventualities [11]. Here, we upon the updated ontology, using a formal, well-specified validity consider the case of ontologies expressed in RDF/S (as most of the model, and then to determine the best way to overcome potential Semantic Web Schemas (85,45%) are expressed in RDF/S [14]) and invalidity problems in an automatic way, by exploring the various al- introduce a formal framework to handle the evolution of an ontology ternatives and comparing them using a selection mechanism based given a change operation. on an ordering relation on potential side-effects. In particular, our We pay particular attention to the semantics of change operations formal approach is parameterizable to this relation, thus providing which can, in principle, be either elementary (involving a change in a customizable way to guarantee the determination of the “best” re- a single ontology construct) or composite (involving changes in mul- sult. Although our framework is general, in this paper we focus on a tiple constructs) [5]. Even though RDF/S does not support negation, fragment of the RDF/S model which exhibits interesting properties the problem is far from trivial as inconsistencies may rise due to the for deciding query containment and minimization [10]. To the best of validity rules associated with RDF/S ontologies. In fact, naive set- our knowledge, our implementation is the first one that allows pro- theoretical addition or removal of ontological constructs (i.e., direct cessing any type of change operation, and in a fully automatic way. application of a change) has been acknowledged as insufficient for ontology evolution [4, 6, 12]. 2 PROBLEM FORMULATION Most of the implemented ontology management systems (e.g., [1, 2, 8, 13]), are designed using an ad-hoc approach, that solves the 2.1 Modeling RDF/S, ontologies and updates problems related to each change operation on a per-case basis. More In order to abstract from the syntactic peculiarities of the underly- specifically, they explicitly define a finite, and thus incomplete, set of ing language and develop a uniform framework, we will map RDF change operations that they support, and have determined, a priori, to First-Order Logic (FOL). Table 1 (restricted for presentation pur- the semantics of each such operation. Hence, given the lack of a for- poses) shows the FOL representation of certain RDF statements. mal methodology, the designers of these systems have to determine, The language’s semantics is not carried over during the mapping, in advance, all the possible invalidities that could occur in reaction so we need to combine the FOL representation with a set of validity to a change, the various alternatives for handling any such possible rules that capture such semantics. For technical reasons, we assume invalidity, and to pre-select the preferable solutions for implementa- that all constraints can be encoded in the form of (or can be broken tion per case [6]; this selection is hard-coded into the systems’ im- down into a conjunction of) DEDs (disjunctive embedded dependen- plementations. This approach requires a highly tedious, case-based cies), which have the following general form: reasoning which is error-prone and gives no formal guarantee that 8~uP (~u) !_i=1;:::;n9~viQi(~u;~vi) (DED) 1 Institute of Computer Science, FO.R.T.H., Heraklion, Greece, email:gconstan,fgeo,antoniou,[email protected] where: 2 This work was partially supported by the EU projects CASPAR (FP6-2005- IST-033572) and KP-LAB (FP6-2004-IST-27490). ² ~u,~vi are tuples of variables Table 1. Representation of RDF facts using FOL predicates Table 2. Validity Rules RDF triple Intuitive meaning Predicate Rule ID/Name Integrity Constraint Intuitive Meaning C rdf:type rdfs:Class C is a class CS(C) R2 Domain 8x; y 2 §: Domain applies to prop- P rdf:type rdf:Property P is a property PS(P ) Applicability Domain(x; y) ! erties; the domain of a x rdf:type rdfs:Resource x is a class instance CI(x) PS(x) ^ CS(y) property is a class P rdfs:domain C domain of property Domain(P; C) R4 C IsA 8x; y 2 §: Class IsA applies be- P rdfs:range C range of property Range(P; C) Applicability C IsA(x; y) ! tween classes C1 rdfs:subClassOf C2 IsA between classes C IsA(C1;C2) CS(x) ^ CS(y) P1 rdfs:subPropertyOf P2 IsA between properties P IsA(P1;P2) R6 C Inst 8x; y 2 §: Class Instanceof applies x rdf:type C class instantiation C Inst(x; C) Applicability x P y property instantiation PI(x; y; P ) C Inst(x; y) ! between a class instance CI(x) ^ CS(y) and a class R8 Domain is 8x; y; z 2 §: The domain of a prop- unique Domain(x; y) ! erty is unique ² P , Qi are conjunctions of relational atoms of the form :Domain(x; z) _ (y = 0 z) R(w1; :::; wn) and equality atoms of the form (w = w ), where R10 Domain and 8x 2 §; 9y; z 2 §: Each property has a do- 0 w1; :::; wn, w, w are variables or constants Range exists PS(x) ! main and a range ² P may be the empty conjunction Domain(x; z) ^ Range(x; y) R11 C IsA 8x; y; z 2 §: Class IsA is Transitive We employ DEDs, as they are expressive enough for capturing the Transitivity C IsA(x; y) ^ semantics of different RDF fragments and other simple data mod- C IsA(y; z) ! els which are appropriate for our purposes in this paper. Moreover, C IsA(x; z) R12 C IsA 8x; y; 2 §: Class IsA is Irreflexive DEDs will prove suitable for constructing a convenient mechanism Irreflexivity C IsA(x; y) ! for detecting and repairing invalidities. :C IsA(y; x) R15 Determining 8x; y; z 2 §: Class instance propaga- Table 2 shows some rules that are used to capture the semantics of C Inst C Inst(x; y) ^ tion the various RDF constructs (e.g., R11 captures IsA transitivity), as C IsA(y; z) ! C Inst(x; z) well as the restrictions imposed by our RDF model (e.g., R8 captures R17 Property 8x; y; z; w 2 §: Instanceof between that the domain of a property should be unique). It should be stressed Instance of and PI(x; y; z) ^ properties reflect in their Domain sources/domains that the semantics of the language captured by tables 1 and 2 essen- Domain(z; w) ! 3 C Inst(x; w) tially corresponds to a fragment of the standard RDF/S data model R23 P IsA 8x; y 2 §: Property IsA is Irreflex- in which there is a clear role distinction between ontology prim- Irreflexivity P IsA(x; y) ! ive :P IsA(y; x) itives, no cycles in the subsumption relationships, while property subsumption respects corresponding domain/range subsumption re- lationships. Such a fragment has been first studied in [10] in an effort positive ground facts that are already in the ontology. The above two to provide a group of sound and complete algorithms for query con- properties together with the CWA semantics, imply that: tainment and minimization while it is compatible with W3C guide- lines4 for devising restricted fragments of the RDF/S data model. ² P (x) 2 K , K ` P (x) , K 0 :P (x) Similarly, the general-purpose change handling algorithm presented ² P (x) 2= K , K ` :P (x) , K 0 P (x) in this paper can be also applied to other fragments of RDF/S (see An application of these properties is that updating K with :P (x) also [7, 9]) or the standard RDF/S semantics.