I imagine that what you need is to know when entering an event if the responsable
has already assigned another event in the date range between start
and end
If so, what you could do is consult prior to the insertion of a tuple in event as follows:
Assuming that in your application at the time of this check you have 3 variables with the values to consult
param_start
start date of the period of the new event to be inserted
param_end
end date of the period of the new event to be inserted '
param_responsable
identifier of the person responsible for whom you want to insert a new event
select 1 from event where idresponsable = param_responsable and ((start between param_start and param_end) or (end between param_start and param_end))
In this way, if this query yields results, it means that the person in charge has an event such that some of the start or end dates of the new event to be inserted fall within the range of the previous event, which would make its presence impossible.