A Metric Temporal Logic for Dealing with Zero-Time Transitions

Many industrial systems include components interacting with each other that evolve with possibly very different speeds. To deal with this situation many formalisms adopt the abstraction of ``zero-time transitions´´, which do not consume time. These, however, have several drawbacks in terms of naturalness and logic consistency, as a system is modeled to be in different states at the same time. We introduce a metric temporal logic, called X-TRIO, that uses non-standard analysis to elegantly deal with zero-time transitions in an abstract, descriptive way. We study the decidability of the logic, and we introduce a decision procedure for a subset thereof. X-TRIO has been applied in companion works to the design and verification of industrial systems.