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
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This paper presents an inference algorithm that can discover temporal logic properties of a system from data. Our algorithm operates on finite time system trajectories that are labeled according to whether or not they demonstrate some desirable system properties (e.g. "the car successfully stops before hitting an obstruction"). A temporal logic formula that can discriminate between the desirable behaviors and the undesirable ones is constructed. The formulae also indicate possible causes for each set of behaviors (e.g. "If the speed of the car is greater than 15 m s within 0.5s of brake application, the obstruction will be struck") which can be used to tune designs or to perform on-line monitoring to ensure the desired behavior. We introduce reactive parameter signal temporal logic (rPSTL), a fragment of parameter signal temporal logic (PSTL) that is expressive enough to capture causal, spatial, and temporal relationships in data. We define a partial order over the set of rPSTL formulae that is based on language inclusion. This order enables a directed search over this set, i.e. given a candidate rPSTL formula that does not adequately match the observed data, we can automatically construct a formula that will fit the data at least as well. Two case studies, one involving a cattle herding scenario and one involving a stochastic hybrid gene circuit model, are presented to illustrate our approach.