We consider a modal language for affine planes, with two sorts of formulas (for points and lines) and three modal boxes. To evaluate formulas, we regard an affine plane as a Kripke frame with two sorts (points and lines) and three modal accessibility relations, namely the point-line and line-point incidence relations and the parallelism relation between lines. We show that the modal logic of affine planes in this language is not finitely axiomatisable.

For efficient energy distribution, microgrids provide significant assistance to main grids and act as a bridge between the power generation and consumption. Renewable energy generation resources, particularly photovoltaics, are considered as a clean source of energy but are highly complex, volatile, and intermittent in nature making their forecasting challenging. Thus, a reliable, optimized, and a robust forecasting method deployed at MG objectifies these challenges by providing accurate renewable energy production forecasting and establishing a precise power generation and consumption matching at (...) MG. Furthermore, it ensures effective planning, operation, and acquisition from the main grid in the case of superior or inferior amounts of energy, respectively. Therefore, in this work, we develop an end-to-end hybrid network for automatic PV power forecasting, comprising three basic steps. Firstly, data preprocessing is performed to normalize, remove the outliers, and deal with the missing values prominently. Next, the temporal features are extracted using deep sequential modelling schemes, followed by the extraction of spatial features via convolutional neural networks. These features are then fed to fully connected layers for optimal PV power forecasting. In the third step, the proposed model is evaluated on publicly available PV power generation datasets, where its performance reveals lower error rates when compared to state-of-the-art methods. (shrink)