Temporal prophecy for proving temporal properties of infinite-state systems

Various verification techniques for temporal properties transform temporal verification to safety verification. For infinite-state systems, these transformations are inherently imprecise. That is, for some instances, the temporal property holds, but the resulting safety property does not. This paper introduces a mechanism for tackling this imprecision. This mechanism, which we call temporal prophecy, is inspired by prophecy variables. Temporal prophecy refines an infinite-state system using first-order linear temporal logic formulas, via a suitable tableau construction. For a specific liveness-to-safety transformation based on first-order logic, we show that using temporal prophecy strictly increases the precision. Furthermore, temporal prophecy leads to robustness of the proof method, which is manifested by a cut elimination theorem. We integrate our approach into the Ivy deductive verification system, and show that it can handle challenging temporal verification examples.

Distributed temporal graph analytics with GRADOOP

Temporal property graphs are graphs whose structure and properties change over time. Temporal graph datasets tend to be large due to stored historical information, asking for scalable analysis capabilities. We give a complete overview of Gradoop, a graph dataflow system for scalable, distributed analytics of temporal property graphs which has been continuously developed since 2005. Its graph model TPGM allows bitemporal modeling not only of vertices and edges but also of graph collections. A declarative analytical language called GrALa allows analysts to flexibly define analytical graph workflows by composing different operators that support temporal graph analysis. Built on a distributed dataflow system, large temporal graphs can be processed on a shared-nothing cluster. We present the system architecture of Gradoop, its data model TPGM with composable temporal graph operators, like snapshot, difference, pattern matching, graph grouping and several implementation details. We evaluate the performance and scalability of selected operators and a composed workflow for synthetic and real-world temporal graphs with up to 283 M vertices and 1.8 B edges, and a graph lifetime of about 8 years with up to 20 M new edges per year. We also reflect on lessons learned from the Gradoop effort.

Temporal enhancement of cross-adaptation between density and size perception based on the theory of magnitude

The estimation of spatial distances is one of the most important perceptual outputs of vision and can easily be deduced even with detached objects. However, how the visual system encodes distances between objects and object sizes is unclear. Hisakata, Nishida, and Johnston (2016) reported a new adaptation effect, in which the perceived distance between objects and the size of an object shrink after adaptation to a dense texture. They proposed that the internal representation of density plays a role in a spatial metric system that measures distance and size. According to the theory of magnitude (Walsh, 2003), the estimation of spatial extent (distance and size) shares common metrics with the estimation of temporal length and numerosity magnitudes and is processed at the same stage. Here, we show the existence of temporal enhancement in cross-adaptation between density and size perception. We used the staircase method to measure the temporal property. The test stimuli were two circles, and the adapting stimulus had a dotted texture. The adapting texture refreshed every 100 or 300 ms, or not at all (static), during the adaptation. The results showed that the aftereffects from a refreshing stimulus were larger than those under the static condition. On the other hand, density adaptation lacked such enhancement. This result indicates that repetitive presentation of an adapting texture enhanced the density–size cross-aftereffect. According to the theory of magnitude, a common mechanism encodes spatial and temporal magnitude estimation and the adaptation to temporal density explains this cross-adaptation enhancement.

Wyclif, John (c.1330–84)

John Wyclif was a logician, theologian and religious reformer. A Yorkshireman educated at Oxford, he was first prominent as a logician; he developed some technical notions of the Oxford Calculators, but reacted against their logic of terms to embrace with fervour the idea of the real existence of universal ideas. He expounded his view as a theologian, rejecting the notion of the annihilation of substance (including the eucharistic elements) and treating time as merely contingent. The proper understanding of universals became his touchstone of moral progress; treating scripture as a universal idea, he measured the value of human institutions, including the Church and its temporal property, by their conformity with its absolute truth. These views, though temporarily favoured by King Edward III, were condemned by Pope Gregory XI in 1377 and by the English ecclesiastical hierarchy in 1382, forcing him into retirement but leaving him the inspirer of a clandestine group of scholarly reformers, the Lollards.