Based on weighted possible-world semantics, Belle and Lakemeyer recently proposed the logic DS, a probabilistic extension of a modal variant of the situation calculus with a model of belief. The logic has many desirable properties like full introspection and it is able to precisely capture the beliefs of a probabilistic knowledge base in terms of the notion of only-believing. While the proposal is intuitively appealing, it is unclear how to do planning with such logic. The reason behind this is that the logic lacks projection reasoning mechanisms. Projection reasoning, in general, is to decide what holds after actions. Two main solutions to projection exist: regression and progression. Roughly, regression reduces a query about the future to a query about the initial state while progression, on the other hand, changes the initial state according to the effects of actions and then checks whether the formula holds in the updated state. In this paper, we study projection by progression in the logic DS. It is known that the progression of a categorical knowledge base wrt a noise-free action corresponds to what is only-known after that action. We show how to progress a type of probabilistic knowledge base wrt noisy actions by the notion of only-believing after actions. Our notion of only-believing is closely related to Lin and Reiter's notion of progression.
Metallic micro/nanostructures present a wide range of applications due to the small size and superior performances. In order to obtain high-performance devices, it is of great importance to develop new methods for preparing metallic micro/nanostructures with high quality, low cost, and precise position. It is found that metallic micro/nanostructures can be obtained by scratch-induced directional deposition of metals on silicon surface, where the mask plays a key role in the process. This study is focused on the preparation of keto-aldehyde resin masks and their effects on the formation of scratch-induced gold (Au) micro/nanostructures. It is also found that the keto-aldehyde resin with a certain thickness can act as a satisfactory mask for high-quality Au deposition, and the scratches produced under lower normal load and less scratching cycles are more conducive to the formation of compact Au structures. According to the proposed method, two-dimensional Au structures can be prepared on the designed scratching traces, providing a feasible path for fabricating high-quality metal-based sensors.
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