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Conflict detection and analysis are of high importance, e.g., when integrating conceptual schemata, such as UML-Specifications, or analysing goal-fulfilment of sets of autonomous agents. In general, models for this introduce unnecessarily complicated frameworks with several disadvantages regarding semantics as well as complexity. This paper demonstrates that an important set of static and dynamic conflicts between specifications can be diagnosed using ordinary first-order modal logic. Furthermore, we show how the framework can be extended for handling situations when there are convex sets of probability measures over a state-space. Thus, representing specifications as conceptual schemata and using standard Kripke models of modal logic, augmented with an interval-valued probability measure, we propose instrumental definitions and procedures for conflict detection.