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This paper extends the formalism of prioritized synchronous composition (PSC), introduced by Heymann, for modeling interaction (and control) of discrete event systems to incorporate partial observation. PSC based control helps remove the control-compatibility requirement of a supervisor. In order to also remove the observation-compatibility requirement of a supervisor, there have been attempts to generalize PSC to account for partial observation. First such attempt was the notion of masked composition (MC), and later the notion of masked-PSC (MPSC) was introduced. Under MPSC the condition for existence of supervisor is normality together with controllability, as opposed to the usual weaker condition of observability together with controllability. This motivates the introduction of the notion of prioritized synchronous composition under mask (PSCM). We show that when PSCM is adopted as a mechanism of interaction, not only the control and observation-compatibility requirements are removed of a supervisor, the existence condition is given by achievability that is weaker than controllability and observability combined. (The weaker condition is required since we allow supervisors to be nondeterministic.) This suggests that the notion of PSCM, presented in the paper is an appropriate generalization of PSC to account for partial observation.