We present a modal logic for subject-oriented representation and reasoning about a two-dimensional space, which we call $\mathsf{SOSL}$. The space is represented with the polar coordinate system where the subject occupies the central point and modal operators are interpreted by relations defined relatively to the position and orientation of the subject, namely ‘outwards’, ‘inwards’, ‘clockwise’, ‘counter-clockwise’, and the transitive closures of the first two. Such logic enables to express operators for the intrinsic relations: ‘in front’, ‘behind’, ‘to the left’, and ‘to the right’ of the subject, for the relative relations: ‘behind an object’, ‘between the subject and an object’, ‘to the left of an object’, and ‘to the right of an object’, and hybrid or distance operators. We prove that the satisfiability problem in $\mathsf{SOSL}$ is PSpace-complete, the same complexity holds over the classes of finite or infinite models, however, for models of fixed size the problem becomes NP-complete.

我们提出了一种用于面向主题的表示和关于二维空间的推理的模态逻辑，我们称之为 $\mathsf{紧急救援队}$. 空间用极坐标系表示，其中主体占据中心点，模态运算符由相对于主体的位置和方向定义的关系来解释，即“向外”、“向内”、“顺时针”、“逆向”。顺时针'，以及前两个的传递闭包。这种逻辑能够表达内在关系的运算符：主体的“前面”、“后面”、“左边”和“右边”，对于相对关系：“在一个对象后面”、“在对象之间”主体和客体”、“客体左侧”和“客体右侧”，以及混合或距离运算符。我们证明了可满足性问题$\mathsf{紧急救援队}$是PSpace -complete，相同的复杂度适用于有限或无限模型的类别，但是，对于固定大小的模型，问题变为NP -complete。