Animals learn to predict external contingencies from experience through a process of conditioning. A natural mechanism for conditioning is stimulus substitution, whereby the neuronal response to a stimulus with no prior behavioral significance becomes increasingly identical to that generated by a behaviorally significant stimulus it reliably predicts. We propose a recurrent neural network model of stimulus substitution which leverages two forms of inductive bias pervasive in the cortex: representational inductive bias in the form of mixed stimulus representations, and architectural inductive bias in the form of two-compartment pyramidal neurons that have been shown to serve as a fundamental unit of cortical associative learning. The properties of these neurons allow for a biologically plausible learning rule that implements stimulus substitution, utilizing only information available locally at the synapses. We show that the model generates a wide array of conditioning phenomena, and can learn large numbers of associations with an amount of training commensurate with animal experiments, without relying on parameter fine-tuning for each individual experimental task. In contrast, we show that commonly used Hebbian rules fail to learn generic stimulus-stimulus associations with mixed selectivity, and require task-specific parameter fine-tuning. Our framework highlights the importance of multi-compartment neuronal processing in the cortex, and showcases how it might confer cortical animals the evolutionary edge.