Inspired by cognitive and neurological literature on action ownership and action awareness, in this paper a computational cognitive model for intentional inhibition (i.e.; the capacity to voluntarily suspend or inhibit an action) is introduced. The interplay between (positive) potential selection of an action, and (negative) predicted impact of this action is addressed. Neurological evidence indicates that this interplay of positive and negative influences on action selection has contributed to make a homo sapiens into a social being. In this process performative and constitutive desires are used to differentiate the influence for action preparation and intentional inhibition with the relevant supportive states: ownership and awareness states. Intentional inhibition is different from action inhibition processes related to an externally guided stop signal. In intentional inhibition process mainly an internally guided action is inhibited through an internally guided stop signal. The proposed model was validated through five scenarios by using a generic parameter value set which is identified through a systematic analytical approach. These scenarios cover the situations in which the agent is: (1) intentionally inhibited action with satisfactory predicted action effect, (2) unable to intentionally inhibit an action with satisfactory predicted action effect, (3) influence of impact prediction on intentional inhibition process, (4) action selection and inhibition in a fully unconscious situation, and (5) impact of the lack of constitutive desires in the effect prediction process. The introduced computational model provides a basis for application domains concerning decision making, behavioral management, emotional control, and simulations for clinical disorders and therapies for them.