A system model of the primate neocortex is presented, based mainly on the neuroanatomy of the rhesus macaque monkey and consisting of a set of processing modules arranged as a perception-action hierarchy. These modules correspond to regions of the neocortex and their connectivity to that of the neocortex. A computational approach based on predicate logic is explained, and the results of a computer implementation of the model are reported, which demonstrate social behaviors involving affiliation and social conflict. The behavioral states of primates involved in these behaviors can be represented by the states of the system model, which have a logical representation and a diagrammatic form. It is shown how the behavioral states in goal-directed behaviors can be represented and also their short term moment-to-moment development in time. It is then shown how the state of social interaction among two or more primates can be represented, using their individual behavioral states, with interindividual action and perception. The causal dynamics of behavioral states is explained and also a control mechanism, namely, the use of confirmation signals, which stabilizes behavioral states and their dynamics. Stabilized behavioral states are seen as corresponding to coherent activations of the system, resulting from successful selection of module activations and intermodule communication with confirmation.