After a brief orientation to logic-based (computational) cognitive modeling, the necessary preliminaries are discussed in this chapter (e.g., what a logic is, and what it is for one to “capture" human cognition are explained). Three “microworlds" or domains that all readers should be comfortably familiar with (natural numbers and arithmetic; everyday vehicles; and residential schools, e.g., colleges and universities) are introduced, in order to facilitate exposition in the chapter. Then the ever-expanding universe U of formal logics, with an emphasis on three categories therein, is given: deductive logics having no provision for directly modeling cognitive states; nondeductive logics suitable for modeling rational belief through time without machinery to directly model cognitive states such as believes and knows; and finally, nondeductive logics that enable the kind of direct modeling of cognitive states absent from the first two types of logic. Then, there follows a focus spcifically on two important aspects of human-level cognition to be modeled in logic-based fashion: the processing of quantification, and defeasible (or nonmonotonic) reasoning. Finally, a brief evaluation of logic-based cognitive modeling is provided, together with some comparison to other approaches to cognitive modeling, and the future of the discipline is considered. The chapter presupposes nothing more than high-school mathematics of the standard sort on the part of the reader.