Modal Logics that Bound the Circumference of Transitive Frames

For each natural number $n$ we study the modal logic determined by the class of transitive Kripke frames in which there are no cycles of length greater than $n$ and no strictly ascending chains. The case $n=0$ is the G\"odel-L\"ob provability logic. Each logic is axiomatised by adding a single axiom to K4, and is shown to have the finite model property and be decidable. We then consider a number of extensions of these logics, including restricting to reflexive frames to obtain a corresponding sequence of extensions of S4. When $n=1$, this gives the famous logic of Grzegorczyk, known as S4Grz, which is the strongest modal companion to intuitionistic propositional logic. A topological semantic analysis shows that the $n$-th member of the sequence of extensions of S4 is the logic of hereditarily $n+1$-irresolvable spaces when the modality $\Diamond$ is interpreted as the topological closure operation. We also study the definability of this class of spaces under the interpretation of $\Diamond$ as the derived set (of limit points) operation. The variety of modal algebras validating the $n$-th logic is shown to be generated by the powerset algebras of the finite frames with cycle length bounded by $n$. Moreover each algebra in the variety is a model of the universal theory of the finite ones, and so is embeddable into an ultraproduct of them

On-line planning and scheduling: an application to controlling modular printers

We present a case study of artificial intelligence techniques applied to the control of production printing equipment. Like many other real-world applications, this complex domain requires high-speed autonomous decision-making and robust continual operation. To our knowledge, this work represents the first successful industrial application of embedded domain-independent temporal planning. Our system handles execution failures and multi-objective preferences. At its heart is an on-line algorithm that combines techniques from state-space planning and partial-order scheduling. We suggest that this general architecture may prove useful in other applications as more intelligent systems operate in continual, on-line settings. Our system has been used to drive several commercial prototypes and has enabled a new product architecture for our industrial partner. When compared with state-of-the-art off-line planners, our system is hundreds of times faster and often finds better plans. Our experience demonstrates that domain-independent AI planning based on heuristic search can flexibly handle time, resources, replanning, and multiple objectives in a high-speed practical application without requiring hand-coded control knowledge

FlowLens: Seeing Beyond the FoV via Flow-guided Clip-Recurrent Transformer

Limited by hardware cost and system size, camera's Field-of-View (FoV) is not always satisfactory. However, from a spatio-temporal perspective, information beyond the camera's physical FoV is off-the-shelf and can actually be obtained "for free" from the past. In this paper, we propose a novel task termed Beyond-FoV Estimation, aiming to exploit past visual cues and bidirectional break through the physical FoV of a camera. We put forward a FlowLens architecture to expand the FoV by achieving feature propagation explicitly by optical flow and implicitly by a novel clip-recurrent transformer, which has two appealing features: 1) FlowLens comprises a newly proposed Clip-Recurrent Hub with 3D-Decoupled Cross Attention (DDCA) to progressively process global information accumulated in the temporal dimension. 2) A multi-branch Mix Fusion Feed Forward Network (MixF3N) is integrated to enhance the spatially-precise flow of local features. To foster training and evaluation, we establish KITTI360-EX, a dataset for outer- and inner FoV expansion. Extensive experiments on both video inpainting and beyond-FoV estimation tasks show that FlowLens achieves state-of-the-art performance. Code will be made publicly available at https://github.com/MasterHow/FlowLens.Comment: Code will be made publicly available at https://github.com/MasterHow/FlowLen

Elementary Canonical Formulae: A Survey on Syntactic, Algorithmic, and Modeltheoretic Aspects

In terms of validity in Kripke frames, a modal formula expresses a universal monadic second-order condition. Those modal formulae which are equivalent to first-order conditions are called elementary. Modal formulae which have a certain persistence property which implies their validity in all canonical frames of modal logics axiomatized with them, and therefore their completeness, are called canonical. This is a survey of a recent and ongoing study of the class of elementary and canonical modal formulae. We summarize main ideas and results, and outline further research perspectives