Despite the current wealth of high-throughput data, our understanding of signal transduction is still incomplete. Mathematical modeling can be a tool to gain an insight into such processes. Detailed biochemical modeling provides deep understanding, but does not scale well above relatively a few proteins. In contrast, logic modeling can be used where the biochemical knowledge of the system is sparse and, because it is parameter free (or, at most, uses relatively a few parameters), it scales well to large networks that can be derived by manual curation or retrieved from public databases. Here, we present an overview of logic modeling formalisms in the context of training logic models to data, and specifically the different approaches to modeling qualitative to quantitative data (state) and dynamics (time) of signal transduction. We use a toy model of signal transduction to illustrate how different logic formalisms (Boolean, fuzzy logic and differential equations) treat state and time. Different formalisms allow for different features of the data to be captured, at the cost of extra requirements in terms of computational power and data quality and quantity. Through this demonstration, the assumptions behind each formalism are discussed, as well as their advantages and disadvantages and possible future developments.