Superconducting logic offers the potential to perform computation at tremendous speeds and energy savings. However, a "semantic gap" lies between the level-driven logic that traditional hardware designs accept as a foundation and the pulse-driven logic that is naturally supported by the most compelling superconducting technologies. A pulse, unlike a level signal, will fire through a channel for only an instant. Arranging the network of superconducting components so that input pulses always arrive simultaneously to "logic gates'' to maintain the illusion of Boolean-only evaluation is a significant engineering hurdle. In this paper, we explore computing in a new and more native tongue for superconducting logic: time of arrival. Building on recent work in delay-based computations we show that superconducting logic can naturally compute directly over temporal relationships between pulse arrivals, that the computational relationships between those pulse arrivals can be formalized through a functional extension to a temporal predicate logic used in the verification community, and that the resulting architectures can operate asynchronously and describe real and useful computations. We verify our hypothesis through a combination of detailed analog circuit models, a formal analysis of our abstractions, and an evaluation in the context of several superconducting accelerators.