We present a logic, (mathbf {ELI^r}), for the discovery of deterministic causal regularities starting from empirical data. Our approach is inspired by Mackie’s theory of causes as INUS-conditions, and implements a more recent adjustment to Mackie’s theory according to which the left-hand side of causal regularities is required to be a minimal disjunction of minimal conjunctions. To derive such regularities from a given set of data, we make use of the adaptive logics framework. Our knowledge of deterministic causal regularities is, as Mackie noted, most often gappy or elliptical. The adaptive logics framework is well-suited to explicate both the internal and the external dynamics of the discovery of such gappy regularities. After presenting (mathbf {ELI^r}), we first discuss these forms of dynamics in more detail. Next, we consider some criticisms of the INUS-account and show how our approach avoids them, and we compare (mathbf {ELI^r}) with the CNA algorithm that was recently proposed by Michael Baumgartner.