UK pensions taxable in Luxembourg only?

Hi helptaxqueries,
The terms 'may' and 'shall' when applied to double taxation agreements, convey two meanings.
'May' is used to allow more than one option, such as 'may be taxable', depending on a set of conditions.
'Shall' is stating an intent, based on the article it relates to, e.g. 'This Convention shall apply to persons who are residents of one or both of the Contracting States'.  
The UK / Luxembourg double taxation agreement states residents of Luxembourg, who have a non government UK private pension, are only taxable on that pension in Luxembourg.
Paragraph 2 of article 18, states that residents of Luxembourg, who have a UK State Pension, are taxable on that pension in the UK, unless they are a national and resident of Luxembourg, in which case it is taxable in Luxembourg.
Thank you.