 Various temporal-epistemic logics were developed during the 1980s, with a unifying study by Halpern and Vardi (1989). They consider a variety of 96 temporal-epistemic logics on so-called interpreted systems, i.e. sets of runs in a transition system with epistemic indistinguishability relations on the state space for each agent. The variety is based on several parameters: number of agents (one or many), the language (with or without common knowledge), the formal model of time (linear or branching time), recall abilities (no recall, bounded recall, or perfect recall), learning abilities (learning or no learning), synchrony (synchronous or asynchronous), unique initial state. Depending on the particular choice of these parameters, the computational complexity of the decision problem for these logics ranges very broadly from PSPACE-complete to highly undecidable (\(\Pi^{1}_{1}\)-complete). For details, see Halpern and Vardi (1989); Fagin et al. (1995); as well as the more recent van Benthem and Pacuit (2006), which surveys a number of decidability and undecidability results for temporal-epistemic logics and illustrates how the combination of time with other modalities bears on computational complexity.