Relational semantics represents an established approach to the study of modal logics. After defining the fundamental syntactic and semantic notions, we examine some basic correspondences between properties of relations and the modal axioms to which they correspond. We introduce normal modal logics and prove soundness and completeness for the basic normal modal system $\textbf{K}$. We then turn our attention to the topological semantics of the modal system $\textbf{S4}$ and, using a construction based on sheaves, extend it to first-order logic. We also consider an example of a schema refuted by a concrete model. In addition to the basic modal language, we address, where appropriate, examples in the basic temporal language. In addition to the basic modal language, we address, where appropriate, examples in the basic temporal language.
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