Today's syndication approaches still provide relatively weak expressive power from a modeling perspective (i.e., XML and RDF are inexpressive modeling languages) and provide very little automated reasoning support. However, if a more expressive approach with formal semantics can be provided, many benefits can be achieved; these include a rich semantics-based mechanism for expressing subscriptions and published content, allowing increased selectivity and finer grained control for filtering . Additionally, automated reasoning can be utilized for discovering subscription matches that cannot be found using traditional syntactic syndication approaches.
In this work, we consider using the Web Ontology Language (OWL) for representing published content. As the semantics of a large subset of OWL is aligned with description logics (DLs), reasoning techniques for DLs can then be leveraged for matching content with subscription requests [9,22,17]. In such an approach, the previously mentioned benefits of using a formal representation language can therefore be achieved. An additional benefit of an OWL-based syndication approach is its native Web embedding and power as a data integration language. Further, such an approach can be seen as a natural extension of existing RSS 1.0 syndication systems, as OWL can be encoded in RDF.
To demonstrate the increased expressivity of an OWL-based syndication approach, consider the following example related to the financial domain. Assume that a stock trader is interested in information contained in news articles (or collections of articles) that discuss news about companies that will make their stocks volatile (i.e., they become risky investments). In particular, assume that the trader is interested in any RiskyCompany that he or she defines to include companies that had their credit downgraded by either Moodys or S&P credit agency and exists on some sell ratings list of a financial institution. Using an XML-based approach, syndication brokers can provide an XML Schema that contains an element RiskyCompany and such companies can be declared to be this type of element. However, more complex logical definitions and automatic classification of objects cannot be supported; therefore, an XML-based approach cannot accommodate the previous example. If we consider an RDF-based approach, then a syndication broker can model the financial domain using RDF Schema; therefore, slightly more complex subscription matches can be obtained, as one can logically infer that a company is a RiskyCompany (e.g., based on subclass relationships). However, in an RDF-based approach, complex logical definitions, such as the previously mentioned RiskyCompany, are not definable. In contrast, in an OWL-based approach, such expressivity is easily provided. For example, RiskyCompany is defined in Table 1 (turtle syntax).
The definitions that the property movedToJunk is a sub-property of downgradedBy, and onRecommendation is the inverse of hasRecommentation, are included in Table 1 as they are used later in the paper.
While OWL-based syndication approaches provide increased expressivity over XML and RDF, previous DL-based syndication approaches suffer from scalability issues due to the inherent complexity of DL reasoning [22,17,9]. This is an issue in domains such as the syndication of financial news feeds because response times must be minimal as critical information must be delivered in near real time (e.g., for stock trading purposes). One of the main limitations in an OWL-based syndication approach is related to DL reasoning over changing data; this is primarily due to the static nature of existing DL reasoning techniques. In particular, the addition of information from newly published documents and data can be viewed as a change in the underlying knowledge base (KB). In current DL reasoning algorithms, reasoning on the updated KB is performed from scratch. The consistency of the KB must be ensured; queries must be re-evalutated; etc. This negatively impacts the performance results of existing DL-based syndication approaches, as performance times are in the tens of seconds. An additional limitation of OWL-based syndication approaches is related to the infancy of the underlying architectures investigated to date; in particular, these architectures have not been investigated in great depth or fully formalized.
In this paper we address both of the previously discussed shortcomings with OWL-based syndication systems. In particular, we first formalize a DL-based syndication framework. We then address the scalability of DL reasoning for the purpose of syndication. First, we present a technique for incremental consistency checking for a substantial portion of OWL. Then, we address the issue of continuous query answering over OWL KBs that are being updated, primarily focusing on reducing the size of the KB that must be considered as candidate query bindings. This effectively allows a smaller subset of the KB to be considered for possible subscription matches. The techniques we present are applicable to queries with at least one distinguished variable (i.e., must be bound to a named individual) and containing only simple roles (i.e., no transitive roles or super-roles of a transitive role). Further, the approach supports the description logic (a large subset of OWL) with the restriction the KB unfoldable (i.e., acyclic). Lastly, an evaluation of the incremental reasoning techniques is provided, demonstrating their effectiveness for OWL-based syndication.
Full proofs of the results presented in this work can be found in the accompanying technical report .
In this section, we briefly provide an overview of OWL and description logics, query answering for DL KBs, and tableau algorithms for DL reasoning.
Let be non-empty and pair-wise disjoint sets of atomic concepts, atomic roles, and individuals respectively. The set of roles (roles, for short) is the set , where denotes the inverse of the atomic role . Concepts are inductively using the following grammar:
A role inclusion axiom is an expression of the form , where are roles. A transitivity axiom is an expression of the form , where . An RBox is a finite set of role inclusion axioms and transitivity axioms. For concepts, a concept inclusion axiom is an expression of the form . A TBox is a finite set of concept inclusion axioms. An ABox is a finite set of concept assertions of the form (where can be an arbitrary concept expression), role assertions of the form and inequality (equality) assertions of the form (respectively ). A KB is composed of TBox , RBox and ABox . Denote the set of individuals in KB (ABox assertion ) as (respectively ).
An interpretation is a pair , where is a non-empty set, called the domain of the interpretation, and is the interpretation function. The interpretation function assigns to a subset of , to each a subset of and to each an element of . The interpretation function is extended to complex roles and concepts as given in .
The satisfaction of a axiom/assertion in an interpretation , denoted is defined as follows: (1) iff ; (2) iff for every , if and , then ; (3) iff ; (4) iff ; (5) iff ; and (6) iff . The interpretation is a model of an RBox (TBox ) if it satisfies all the axioms in (respectively ). is a model of , denoted by , if it satisfies all the assertions in . Lastly, is a model of , denoted by , iff is a model of , , and .
We also introduce the following notation: denote by the set of all models for . Additionally, given a concept , denote by the maximum modal depth for (i.e., the maximum nesting depth of quantifiers).
Lastly, we provide a brief overview of conjunctive ABox queries (query, for short) for description logics. A query consists of a conjunction of ABox assertions of the form or (see  for a precise definition), in which variables can be used in place of individuals and are considered as existentially quantified (the set of variable names, denoted , is assumed to be distinct from the individual names, ). Query answering is the task of determining if is a logical consequence of the KB (denoted ); that is, determining if for all models of , . As query retrieval is addressed in this work, we briefly introduce the following notation (adopted from ): indicates that the variables appearing in must be bound to individual names, therefore constituting the answer to the query. These variables are referred to as distinguished variables, denoted (). The answer set of a query w.r.t. to is the set -ary tuples defined by the following:
In this section we formally define the DL-based syndication framework proposed in this work. As in typical syndication systems, we assume syndication brokers deliver relevant information to the appropriate subscription requests. Within this framework, a subscription is comprised of a conjunctive ABox (instance) query, which represents the subscribers interests, and an expiration time (i.e., the number of time units that the subscription is valid). The subscription query can be thought of as a continuous conjunctive query that should be evaluated until the expiration time. Therefore, the query is issued once over a changing ABox whose results set is continuously updated as the ABox changes. Intuitively, the answer set of a continuous conjunctive ABox query at time is the set of all variable bindings entailed by the KB at time and can be seen as an extension of the definition of a conjunctive query presented earlier.
Given this, a subscription is defined as follows:
We denote the continuous query of a subscription as and the expiration time as . We now define a subscriber to be composed of a set of subscriptions and a unique identifier:
Denote a subscriber's set of subscriptions as , and its identifier as . Next, we define a publisher to be identified by a unique identifier:
Additionally, a publication is defined to be composed of a set of ABox assertions, the number of time units that the publication is valid, and the identifier of the publisher that produced the information; after the specified time units have passed, it is assumed that the publication is discarded.
Given a publication , denote the set of ABox assertions as , the expiration time as , etc. Intuitively, a syndication broker maintains a local KB, in which newly published information is integrated. Additionally, the syndication broker maintains the currently registered subscribers (that have associated subscriptions) and publishers. This is formally defined as follows:
We denote a syndication broker's subscriptions, publishers, and KB as , , and respectively. After a new publication is received, it is the broker's task to determine the subscribers for which this new infromation is relevant. Before defining subscription matches, we define a generic update function that takes a set of publications and integrates them into the broker's KB. Such a function is necessary for integrating newly published information into a DL KB.
Observe that this update function is generic, as there are many different ways to interpret the update. Such problems have been studied extensively in literature for updating logical KBs. We do not impose a particular type of update semantics in the formalization of the syndication framework; rather, we only enforce that the update function result in a consistent KB. This is necessary because if the updated KB is inconsistent, then everything is trivially entailed. In Section 4.1 we define a specific update function, referred to as syntactic updates.
Lastly, we define a match for a subscription request. As information (documents) is published from multiple publishers and remains valid in the broker's local KB for varying time, a match for a subscription can actually be a composition of the information from multiple publications; that is, the information provided in multiple publications collectively forms a match for the query. To the authors' knowledge, recent approaches have not investigated such functionality; rather, only information from individually published documents form a match for a given subscription. However, such a capability is beneficial, as information can be considered collectively and form matches not found otherwise.
We additionally distinguish between two types of subscription matches, namely information matches and publication matches. An information match refers to the individuals bound to the (distinguished) variables of a continuous query representing a subscription; that is, the result returned to the subscriber is actually the query answer rather than the publication(s) responsible for the answer. This type of match aligns with recent work in XML-based syndication literature, in which the actual information is filtered and the query answers are returned to the user . In contrast, a publication match refers to the collection of publications that satisfy a subscription; that is, given an information match for a registered subscription, return all minimal sets of publications that cause this match to occur; this aligns with the task of selective content-based filtering of publications. It is clear that given an information match, there is a corresponding set of publication matches.
The distinction between these two match types is made as additional computation is needed to derive all the minimal sets of publications responsible for an information match. Further, the type of match required is application dependent; for example, in OWL-based syndication of news feeds, it is clear that publication matches are needed. In contrast, in the financial domain, analysts are generally interested with the actual information rather than the documents themselves. If we consider our previous example involving the concept , we can observe that analysts are likely to be more interested in the actual instances of , rather than the articles that discuss them; this is intuitive, as the actual query answer is the actionable information for their purposes (e.g., stock trading). In this work, we address both of these matches; however, our current evaluation focuses on information matches, leaving the remainder as future work. We now define an information match:
Before defining a publication match, we present the notion of minimal justifications for an entailment in DLs, which has been formally investigated in literature .
Now we present the definition of a publication match which utilizes minimal justifications to define to the publications responsible for an information match:
We conclude this section with a brief example demonstrating a composite match (both information and publication matches), and the framework in general. Assume a syndication broker is composed of one subscription and two publishers. Additionally, assume that the broker's local KB contains the axioms defined previously in Table 1. The the broker is composed of the following:
As discussed earlier, the main limitation in the proposed syndication framework is related to DL reasoning through incremental changes to the underlying KB. Therefore, the remainder of this paper addresses the two previously mentioned performance bottlenecks, namely consistency checking and query answering through updates. Before addressing these issues, we present the update function adopted for this work.
For the task of syndication, we propose an update function that
we refer to as syntactic updates, which supports syntactic
changes of KB assertions. Intuitively, syntactic updates can be
described as an update in which all new assertions are directly
added (or removed) to the asserted (base) axioms. For purpose of
this work, ABox assertions can take the form of individual equality
:Fordowl:sameAs:FordMotorCorp) and inequality assertions (e.g., :Moodysowl:differentFrom:SandP), concept assertions (e.g., :Forda:Company; note that complex concept assertions are possible as well), and role assertions (e.g., :Ford:downgradedBy :Moodys). Formally, this is described as follows:
This type of update is different when compared to related work in update semantics  and belief revision  for DLs; however, it is clearly applicable to syndication applications. Further, there have been negative results with respect to other candidate update semantics for DL KBs. In particular,  shows that the standard (minimal change) model-based update semantics cannot be represented in the DLs considered in this paper.  shows that many DLs, including those considered here, cannot satisfy the rationality postulates proposed in the AGM theory of belief revision.
It is clear that under syntactic updates, the resulting KB can be inconsistent after an update; however, as required by Definition 7, the update function must result in a consistent KB. For this work, we assume that if the resulting KB is inconsistent, then the newly published information is rejected (i.e., removed from the KB). While discarding the recent publication may not be the ideal course of action in all syndication systems, addressing this issue further is out of the scope of this paper. However, we plan to address this issue in future work and provide some initial insights in Section 6.
After newly published information is integrated in the broker's KB, consistency must be re-checked. As stated earlier, with large ABoxes, checking consistency introduces substantial overhead. In this case of syndication, this problem is compounded, as the broker's KB will become substantially large because the KB can contain permanent domain knowledge, as well as publications that remain valid for substantial time periods.
To address this issue, we have recently investigated incremental consistency checking in OWL KBs. In particular, in  we present an approach for incrementally updating tableau completion graphs under syntactic ABox updates in the description logics and , which encompass the portion of OWL-DL addressed later in this work. In  the update algorithm adds new (removes existing for deletions) components (edge, nodes, or labels) introduced by the update to a (cached) completion graph from the consistency check prior to the update; after this, standard tableau completion rules are re-fired to ensure that the model is complete. Therefore, the completion graph built prior to the update (e.g., during the initial consistency check) is cached and updated such that if a model exists (i.e, the KB is consistent after the update), a new completion graph will be found. It was observed that updates did not have a large effect on the existing completion graph; therefore, orders of magnitude performance improvements are achieved. Due to space limitations, further details regarding the approach are omitted here; however, they can be found in .
Before discussing the overall goal of the approach, we make a few simplistic observations: by monotonicity of (and OWL-DL in general), continuous query answering in the event of ABox additions reduces to determining any new bindings that are entailed by the KB, whereas handling deletions reduces to guaranteeing that previous bindings are still entailed.
When querying very large ABoxes, one of the main problems is that a large number of individuals in the KB must be considered as potential variable bindings. However, we propose that under the types of updates considered in this work, the candidate query bindings can be drastically pruned. A key insight is demonstrated if we consider a simple query such as x Company(x). Intuitively, in the event an update is an addition, we would only like to consider affected named individuals not previously bound to as potential new bindings (i.e., answers); in contrast if the update is a deletion, only individuals previously bound to that were affected by the update need to be re-checked. Therefore, the main goal of the approach presented here is to localize the named individuals in the KB that are affected by the update in such a way that they may impact the previous query results.
Before discussing this further, we define the notion of explicitly affected individuals, which intuitively are the individuals manipulated during the incremental update of all completions for a KB.
Additionally, we introduce the notion of a root path
between two individuals:
We now define the general notion of affected individuals adopted for the purpose of this work; given these individuals, we show that all new (resp. invalidated) bindings for a query can be found.
It can be shown that for there to be a new (resp. invalidated) binding after an update, at least one named individual in the binding must be in .
Proposition 1 is intuitive as it states that for there to be a new (resp. invalidated) binding, then there must exist some individual in that binding that either is directly affected by the update in some completion graph or is in the proximity of some other individual that was directly affected. We are able to show that the notion of proximity introduced in Proposition 1 (conditions 2 and 3) is sufficient (observe that currently we do not take into account the structure of the concepts in the query; however, we plan to address this in future work). More importantly, Proposition 1 implies that in order to find the affected individuals, one can update all and gather the individuals that satisfy the properties provided.
It is clear, however, that incrementally maintaining all completion graphs for a given KB is not practical; further in the presence of a reasonable degree of non-determinism in a KB, saturating the tableau is a very expensive process. To avoid performing a full saturation of the initial KB, we propose building a structure that we refer to as a summary root graph.
Observe that condition 2 is required, as adding all labels from a disjunction can obviously introduce clashes; also note that only the structure for root nodes and their edges is kept to reduce memory overhead. It can be seen that the summary root graph does not correspond to a model of the KB; however, the approach guarantees that if a root node or edge between root nodes has a label in some completion graph corresponding to a model for the KB, then that label will be in the label set for that individual in the summary root graph. The aim behind the approach is to use this structure to localize an overestimate of the explicitly affected individuals; an overestimate is acceptable as, in the end, we are trying to find only candidate distinguished variable bindings.
Using the summary root graph, an overestimate for can be provided; we first note that in the case of ABox deletions, we propose using axiom tracing [2,15,12] during the application of expansion rules, effectively tracking the asserted axioms responsible for changes to the summary root graph. We also note that there is a small modification when checking if the expansion rules can be applied to a node (to guarantee completeness). Specifically, node labels are marked when they have had a completion rule applied to them during the overestimate procedure; if the label is not marked, then the expansion rule is applied. Details are omitted here, however they can be found in Table 2 of .
Note that after the application of expansion rules finishes, it is assumed that un-named nodes and their edges are discarded from the summary root graph (which has therefore been updated). Additionally, when the summary root graph is updated during an addition, axioms traces are updated using the same approach as in . It can be shown that after the update, the overestimate of the explicitly affected individuals satisfies the following property:
Proposition 2 implies that
we can use to
locate a superset of the affected individuals (defined
Discussion. It is clear that there are possible limitations to the current approach for determining the overestimate of individuals affected by updates. In particular, if the approach produces an overestimate that is too large, the value of the approach may degrade (note that in the worse case, the number of individuals one would have to check is the same as in the non-incremental case). However, our initial results indicate that the approach is extremely effective. An additional limitation of the approach is the memory overhead imposed by maintaining the summary root graph, which is clearly a trade-off in the approach. One last issue is related to the application of expansion rules on the summary root graph with respect to the update. We point out here that in the worst case this could impose overhead that is not practical for the performance demands of some syndication applications; however, our initial results demonstrate that this is not the case. This is because the expansion rules are applied with respect to only the update and not the entire KB. This is actually quite intuitive, as one would expect for updates to only affect a small portion of the KB. Further, if we consider syndication of news feeds for example, one would expect updates to be generally focused on a small number of individuals. This is clearly evident in the financial domain; for example, the Dow Jones Newswires disseminates on average 10,000 news feeds per day3, which are typically terse and focused on specific companies, industries, etc.
We now introduce a technique for determining the query impact on the affected individuals, which is a straightforward approach that induces very little overhead. The key insight is that for a new query binding to be entailed (or invalidated in the case of deletions) under syntactic ABox updates in , at least one named individual that is bound to some must be in . This, along with the facts that the query is assumed to be connected and contain only simple roles, implies that given an addition update, the query impact on the original affected individuals can be taken into account by also considering all named individuals in the updated completion graph (discussed in Section 4.2) that are reachable from some by at most edge traversals (with the direction ignored), where is the longest path in the query graph. Given this, under additions only the various combinations of individuals in this expanded set of affected individuals need to be considered as possible new bindings for distinguished variables. A similar approach can be used to take into account the query impact under deletions, however the original completion graph (prior to its update) must be used for the search of depth (i.e., deletions can remove structures from the completion graph). In the case of deletions, one then needs to re-check any previous binding that contains some individual in the expanded set of affected individuals. Denote by the extended set of affected individuals under this approach for taking into account the query impact.
It is clear that the previous technique does not leverage the actual structure of the query (i.e., concepts and roles in the query); therefore, we now introduce a more effective approach that exploits such information, but also introduces additional overhead. Due to space limitations, the approach is only presented for additions (see  for a discussion regarding deletions); it is also noted that in typical syndication systems, updates are much more frequently additions. We first point out that it has previously been shown that a conjunctive query can be answered be syntactically mapping the query into all completion graphs for the KB . More specifically for the DL (also applicable to ),  shows that given a completion graph and a query , the query can be mapped into , denoted . If the query can be mapped into all completions, then the KB satisfies the query. It can be seen that such a mapping is usable when of taking into account the query impact under additions. We note, however, that such a mapping introduces overhead, as it requires that the KB must be extended with for each concept . In order to further reduce the new candidate bindings, each individual in can be iteratively substituted into variables in the query; neighbor nodes in the updated completion graph can then be inspected to see if they can be mapped into the remaining nodes (via roles whose labels match the query graph) in the query graph (note that distinguished variables in the query graph are mapped into nodes corresponding to named individuals). If there does not exist a mapping in which a given named individual can be mapped into a particular distinguished variable, then this individual does not need to be considered in the candidate distinguished variable set for this variable; this is because we have just found a completion graph (i.e., model) in which the query cannot be mapped . However, if a named individual can be mapped into a distinguished variable, then we must consider this individual as a candidate binding.
Algorithm 1 presents the main continuous query answering algorithm. The approach first locates the affected individuals; this is denoted by and takes as input an initial summary root graph and update and is assumed to both update and return the affected individuals. Additionally, the extended set of affected individuals is found using the the first approach for query impact. If the update is an addition, the set of candidate distinguished variable bindings (determined using Definition 18) is iterated over and checked for entailment. It is assumed that standard techniques for query answering are used (e.g., see ). If the update is a deletion, each tuple in the previous answer set is iterated over; tuples that do not contain some individual in are still valid, as the update did not affect any of the bound individuals. Otherwise, the tuples are re-checked for entailment.
We have performed an emperical evaluation using the Lehigh
University Benchmark (LUBM)  (
expressivity), as it provides a large ABox, therefore simulating a
broker with large numbers of persistent publications; additionally,
it supplies queries with similar complexity as those used in the
examples throughout this paper. It should be noted that 8 OWL
equivalent class axioms were changed to subclass axioms, so that
the KB was unfoldable. Three queries from LUBM were selected as
sample subscriptions and continuously run over a dataset comprised
of one university, containing 16,283 individuals and 78,094
assertions. The following three queries were used in the evaluation
(LUBM queries 1, 3, and 13 respectively):
In the evaluation, the queries were run over the KB, which was updated with a collection of ABox assertions, simulating newly published information; updates were randomly selected individual type (atomic) and/or role assertions, as this aligns with the types of updates one would expect in syndication systems. Each published document was indefinitely valid. To ensure that some of the updates affected the query results (i.e., subscriptions), there was a 50-percent probability that the update referred to one of the individuals bound to a distinguished variable; therefore, approximately half of the selected updates actually affected the subscriptions. Tests were performed for each update type (additions and deletions) using varying update sizes; namely 1, 5, 10, 15, and 25 assertions. Each test was performed 25 times, and the results were averaged. Lastly, the experiments were performed using a 1.5 GHz processor with 1 GB of memory.
In the evaluation, two versions of the DL reasoner Pellet 4 were used; a regular version of the reasoner and an optimized reasoner that used the techniques presented in this paper. In the regular version of the reasoner, the standard query answering algorithm was performed after each update. Additionally, the KAON25 OWL-DL reasoner was used in the evaluation. KAON2 reduces OWL KBs to disjunctive datalog and is optimized for query answering. Additionally, KAON2 was used as it provides functionality to add and remove assertions and re-run queries after a KB has been updated (note that it is unclear whether KAON2 currently performs view maintenance). Therefore, using this as a comparison, we aimed to provide interesting insights into tableau-based algorithms for OWL-based syndication purposes when compared to other possible approaches.
Results for continuous query answering for the various LUBM queries are presented in Figure 1. Note that the optimized version of Pellet is denoted as ``Pellet-C'', and the ``0'' update size value represents the time to run the initial query prior to performing an update (this includes the start-up cost for the continuous query answering approach). In all three queries, the initial query answering time (prior to any update) in the regular version of Pellet was slightly better than the optimized version. This is due to the overhead introduced by the generation of the summary root graph; specifically, the average time to build the summary root graph was 2.7 seconds (on average 500 milliseconds larger than the initial consistency check). We note that there is little overhead because of the small amount non-determinism in LUBM (primarily due to making the KB unfoldable). For exposition, we investigated the time to build the summary root graph for the original version of LUBM, which contains a large amount of non-determinism. It was observed that the average time to build the summary root graph took approximately 26.1 seconds. This demonstrates the expected impact of a substantial amount of non-determinism on the approach; while this introduces overhead, we argue that this is acceptable, as it is only performed once at startup. Further, the generation of the summary root graph was far more efficient than the alternative of saturating the initial KB, as this would not terminate.
For both update types, approximately one to three orders of magnitude performance improvements are achieved over the regular version of Pellet by using the optimized matching algorithm as updates are received. This is due to the incremental consistency checking approach and the reduction of candidate variable bindings. In the evaluation we observed that in all queries, the average incremental consistency checking time was approximately 7 milliseconds, where the normal consistency checking time in Pellet was approximately 2,200 milliseconds. This illustrates the utility of the incremental consistency checking approach for the purpose of syndication. Additionally, in the three queries the actual query answering time (excluding consistency checking) for the regular version of Pellet was on average between 500 to 1,000 milliseconds. In contrast, using the optimizations presented in this work, the average query answering time (excluding consistency checking) was approximately 33 milliseconds; this demonstrates the effectiveness in the reduction of in the number of candidate variable bindings.
With regard to the individual techniques, the evaluation demonstrated the following: given an update of size 1, the average time to apply the completion rules to the updated summary root graph and localize the affected individuals took approximately 0.23 milliseconds. This clearly confirmed our hypothesis that the expansion rules would be applied to only a very small portion of the summary root graph. Even more promising was that the number of affected individuals was proportional to the number of individuals referenced in the update; in particular, for updates of size 1, on average, only 11.144 individuals are affected, amounting to only .068-percent of the entire KB (for increased update size, the number of affected individuals scaled proportionally to the number of individuals referenced in the update). This demonstrates a dramatic reduction in the number of individuals that needed to be considered after each update and shows that the overestimation approach may be usable in practice. Additionally, it can be seen that the optimized version of Pellet outperforms, or performs nearly as well as, KAON2 in all cases. Even more promising is that in query 13, Pellet outperforms KAON2 by almost an order of magnitude.
In this paper, we have primarily addressed providing a more practical approach for finding information matches in OWL-based syndication systems. As mentioned earlier, there has been extensive work on finding minimal justifications in OWL KBs . Using such an approach, it is easy to extend information matches to publication matches. Further, initial results presented in  for finding justifications demonstrates that such an approach may be practical. In future work, we will explore the usage of these techniques for extending our current work.
We also feel that there is substantial room extending the current reasoning approaches. This includes developing additional optimizations for reasoning through changing KBs, as well as extending the current techniques to a larger portion of OWL; in particular, we feel it is certainly possible to lift the restriction that the KB be unfoldable, and we will address this in future work. Additionally, while our initial results demonstrate that the overhead of the advanced form of query impact is acceptable, we plan to further investigate the tradeoffs between the two variants presented here.
Lastly, in real world domains, it is often the case that conflicting information is disseminated. Depending on the ontologies used within such a syndication framework, this could lead to inconsistencies. Currently, we are working on developing revision techniques for OWL-DL KBs and hope to apply such efforts to resolving inconsistencies encountered in syndication systems .
[22,17] proposes a DL-based approach for syndication in which DL concepts are used for both subscription requests as well as published documents/data.  presents a DL-based syndication approach in which the subscriber registers queries (restricted to single, named concepts) that model their interests and published data is modeled as ABox assertions.  also presents two optimizations. First, the authors propose inducing a partial ordering upon all registered queries by their subsumption relations; more general queries are answered first, thereby reducing the number of individuals that must be considered for more specific queries.  also proposes disregarding previous individuals that satisfied registered queries when data is published. Our approach differs as we support complex conjunctive queries, allow subscription and published document expiration times, etc. Additionally, we address the performance bottlenecks of DL-based syndication further.
There has also been substantial work in continuous query answering in relational databases and datalog (e.g., [21,5]). While related, the work presented here addresses a more expressive formalism.
We would like to thank Jennifer Golbeck, Yarden Katz, Vladimir Kolovski, Bijan Parsia, Evren Sirin, and Taowei Wang for all of their contributions to this work. This work was supported by grants from Fujitsu, Lockheed Martin, NTT Corp., Kevric Corp., SAIC, the National Science Foundation, the National Geospatial - Intelligence Agency, DARPA, US Army Research Laboratory, and NIST.
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