The rise of smart applications has drawn interest to logical reasoning over data streams. Recently, different query languages and stream processing reasoning engines were proposed in different communities. However, due to a lack of theoretical foundations, the expressivity and semantics of these diverse approaches are given only informally. Towards clear specifications and means for analytic study, a formal framework is needed to define their semantics in precise terms. To this end, we present a first step towards an ideal semantics that allows for exact descriptions and comparisons of stream reasoning systems.
StreamLog Another logic-based approach towards stream reasoning is StreamLog @cite_11 . It makes use of Datalog and introduces whose first arguments are timestamps. By introducing which have syntactical restrictions on temporal rules, StreamLog defines (for which Closed World Assumption can be safely applied) that can be used in recursive rules in a stream setting. Since sequential programs are locally stratified, they have efficiently computable perfect (i.e., unique) models. Similar to capturing a fragment of Reactive ASP, we can capture StreamLog by converting temporal atoms @math to expressions @math and employing safety conditions to rules to simulate non-blocking negation. Moreover, we plan for having weaker notions of negation that might block rules but just for a bounded number of time points to the future.
@cite_11
1842092674
Data Stream Management Systems (DSMS) have attracted much interest from the database community, and extensions of relational database languages were proposed for expressing continuous queries on data streams. However, while relational databases were built on the solid bedrock of logic, the same cannot be said for DSMS. Thus, a logic-based reconstruction of DSMS languages and their unique computational model is long overdue. Indeed, the banning of blocking queries and the fact that stream data are ordered by their arrival timestamps represent major new aspects that have yet to be characterized by simple theories. In this paper, we show that these new requirements can be modeled using the familiar deductive database concepts of closed-world assumption and explicit local stratification. Besides its obvious theoretical interest, this approach leads to the design of a powerful version of Datalog for data streams. This language is called Streamlog and takes the query and application languages of DSMS to new levels of expressive power, by removing the unnecessary limitations that severely impair current commercial systems and research prototypes. We present Datalog LITE, a new deductive query language with a linear-time model-checking algorithm, that is, linear time data complexity and program complexity. Datalog LITE is a variant of Datalog that uses stratified negation, restricted variable occurrences and a limited form of universal quantification in rule bodies.Despite linear-time evaluation, Datalog LITE is highly expressive: It encompasses popular modal and temporal logics such as CTL or the alternation-free μ-calculus. In fact, these formalisms have natural presentations as fragments of Datalog LITE. Further, Datalog LITE is equivalent to the alternation-free portion of guarded fixed-point logic. Consequently, linear-time model checking algorithms for all mentioned logics are obtained in a unified way.The results are complemented by inexpressibility proofs to the effect that linear-time fragments of stratified Datalog have too limited expressive power. In complex reasoning tasks, as expressible by Answer Set Programming (ASP), problems often permit for multiple solutions. In dynamic environments, where knowledge is continuously changing, the question arises how a given model can be incrementally adjusted relative to new and outdated information. This paper introduces Ticker, a prototypical engine for well-defined logical reasoning over streaming data. Ticker builds on a practical fragment of the recent rule-based language LARS which extends Answer Set Programming for streams by providing flexible expiration control and temporal modalities. We discuss Ticker's reasoning strategies: First, the repeated one-shot solving mode calls Clingo on an ASP encoding. We show how this translation can be incrementally updated when new data is streaming in or time passes by. Based on this, we build on Doyle's classic justification-based truth maintenance system (TMS) to update models of non-stratified programs. Finally, we empirically compare the obtained evaluation mechanisms. This paper is under consideration for acceptance in TPLP. We propose a combination of logic programming under the answer set semantics with the description logics SHIF(D) and SHOIN(D), which underly the Web ontology languages OWL Lite and OWL DL, respectively. To this end, we introduce description logic programs (or dl-programs), which consist of a description logic knowledge base L and a finite set P of description logic rules (or dl-rules). Such rules are similar to usual rules in nonmonotonic logic programs, but they may also contain queries to L, possibly under default negation, in their bodies. They allow for building rules on top of ontologies but also, to a limited extent, building ontologies on top of rules. We define a suite of semantics for various classes of dl-programs, which conservatively extend the standard semantics of the respective classes and coincide with it in absence of a description logic knowledge base. More concretely, we generalize positive, stratified, and arbitrary normal logic programs to dl-programs, and define a Herbrand model semantics for them. We show that they have similar properties as ordinary logic programs, and also provide fixpoint characterizations in terms of (iterated) consequence operators. For arbitrary dl-programs, we define answer sets by generalizing Gelfond and Lifschitz's notion of a transform, leading to a strong and a weak answer set semantics, which are based on reductions to the semantics of positive dl-programs and ordinary positive logic programs, respectively. We also show how the weak answer sets can be computed utilizing answer sets of ordinary normal logic programs. Furthermore, we show how some advanced reasoning tasks for the Semantic Web, including different forms of closed-world reasoning and default reasoning, as well as DL-safe rules, can be realized on top of dl-programs. Finally, we give a precise picture of the computational complexity of dl-programs, and we describe efficient algorithms and a prototype implementation of dl-programs which is available on the Web.