If a person knows that Fred ate a pizza, then they can answer the following questions: Who ate a pizza?, What did Fred eat?, What did Fred do to the pizza? and even Who ate what? This and related properties we are terming accessibility properties for the relational fact that Fred ate a pizza. Accessibility in this sense is a significant property of human cognitive performance. Among neural network models, those employing tensor product networks have this accessibility property. While feedforward networks trained by error backpropagation have been widely studied, we have found no attempt to use them to model accessibility using backpropagation trained networks. This paper discusses an architecture for a backprop net that promises to provide some degree of accessibility. However, while limited forms of accessibility are achievable, the nature of the representation and the nature of backprop learning both entail limitations that prevent full accessibility. Studies of the degradation of accessibility with different sets of training data lead us to a rough metric for learning complexity of such data sets.