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A logic-based foundation of discrete event modeling and simulation is presented by defining (1) its fundamental concepts and terms from a perspective commonly held by logicians, (2) a modal Discrete Event Logic LDE. The ways of expressing models using LDE are discussed and compared with the ways of expressing models in simulation languages that support the event scheduling world view. The logic-based foundation provides fundamentally new insights. It asserts that events are logical propositions and the use of temporal operators is implicit in discrete event modeling and simulation languages. However, existing languages utilize only a few temporal operators in a restricted manner. The logic-based foundation enhances the ways of expressing models by using the operators implicit in existing languages in more general ways, new operators, and a parallel connective ||. The logic LDE and notions implicit in it form a new framework for understanding, defining, and studying logical combinations of events, variables, and time, and expressions containing a wide range of temporal operators including next, if, when, whenever, until, while, unless, and at.