What do people mean by “If there is not beer then there is wine”?

A central question in reasoning research is what computational level principles, if any, people follow when drawing inferences and when making judgments about how strong or weak a particular inference is. Any measure of inference quality depends on the meaning people ascribe to the statements that make up the inference. The statement types with the most contentiously debated meaning in the literature are conditionals. For example, whether the inference “There is beer or wine. Therefore if there is not beer then there is wine” is deductive or not depends on how the conditional that makes up its conclusion is interpreted. Distinguishing between different interpretations of conditionals requires finding situations in which they lead to non-overlapping behavioral predictions. We present a Bayesian latent-mixture model to distinguish between a material conditional, a probabilistic conditional, and a probabilistic biconditional interpretation of conditionals along with a fourth response to capture guessing. The model correctly classifies the responses expected under each interpretation given premise and conclusion probability judgments for six inference types. We simulate data to illustrate the behavior of the model and discuss characteristics of experiments that would be required to distinguish between interpretations.