The article proposes a formal semantics of happiness and sadness modalities in the imperfect information setting. It shows that these modalities are not definable through each other and gives a sound and complete axiomatization of their properties.

Betweenness as a relation between three individual points has been widely studied in geometry and axiomatized by several authors in different contexts. The article proposes a more general notion of betweenness as a relation between three sets of points. The main technical result is a sound and complete logical system describing universal properties of this relation between sets of vertices of a graph.

In the last decades, researchers have been considering some fundamental issues such as energy saving, global warming, greenhouse emissions, and non-renewable energy to make models of house environmental standards to achieve a suitable consumption pattern for saving energy. In architecture, using natural energy is one of the essential pillars of design because it was one of the criteria of designing, which was considered on climate and geography, and it has been a high performance of climate adaptation in the modeling of (...) traditional houses. In this research, Azerbaijan is selected to evaluate the practical features of traditional Iranian houses designed in the cold climate, and criteria for developing sensible solutions to achieve a suitable design model for energy saving are provided. The primary purpose of this paper is to evaluate and identify the features of climate design in traditional houses in a cold climate, which are suitable residential buildings for energy management, and to identify the components affecting energy saving. The data collection method is based on checklists, observation, considering the orientation, density, solar radiation angle in the region, documentary, analysis of maps, and adaptation of the architectural plan of the studied houses with the pattern of solar radiation in the area. This research discusses the design criteria for future structures and their adaptable measures based on the obtained results. Finally, it is declared that the traditional architectural design model follows the region’s climatic conditions, and considering the current climate and energies, traditional houses were designed; therefore, the best model for maximum use of available energy is climatic design. As a result, suggestions are made regarding residential architecture design to save energy. (shrink)