In this paper, a uniform approach for synthesizing monitors checking correctness properties specified in linear-time logics at runtime is provided. Therefore, a generic three-valued semantics is introduced reflecting the idea that prefixes of infinite computations are checked. Then a conceptual framework to synthesize monitors from a logical specification to check an execution incrementally is established, with special focus on resorting to the automata-theoretic approach. The merits of the presented framework are shown by providing monitor synthesis approaches for a variety of different logics such as LTL, the linear-time