A NEURAL ARCHITECTURE FOR A CLASS OF ABDUCTION PROBLEMS

The general task of abduction is to infer a hypothesis that best expla ins a set of data. A typical subtask of this is to synthesize a compos ite hypothesis that best explains the entire data from elementary hypo theses which can explain portions of it. The synthesis subtask of abdu ction is computationally expensive, more so in the presence of certain types of interactions between the elementary hypotheses. In this pape r, we first formulate the abduction task as a nonmonotonic constrained -optimization problem. We then consider a special version of the gener al abduction task that is linear and monotonic. Next, we describe a ne ural network based on the Hopfield model of computation for the specia l version of the abduction task. The connections in this network are s ymmetric, the energy function contains product forms, and the minimiza tion of this function requires a network of order greater than two. We then discuss another neural architecture which is composed of functio nal modules that reflect the structure of the abduction task. The conn ections in this second-order network are asymmetric. We conclude with a discussion of how the second architecture may be extended to address the general abduction task.