Abstract: Highlights•How to extend standard monitor construction to handle non-monitorable properties.•Non-monitorable properties can be partially monitored.•Tackling partial monitorability directly on the monitor makes the approach formalism-agnostic.•A monitor can give up on a property if it recognises it will never conclude its verification.•A monitor can give up on events if such events are not of interest for the verification of the property.
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