Section 5 of the Commercial Arbitration Act 2013 (Qld) does not displace the Supreme Court's inherent jurisdiction to protect claims of Parliamentary privilege and public interest immunity in respect of documents sought to be produced in an arbitration, because such protection is not a 'matter governed by' the CAA. However, the jurisdiction is discretionary: the Court may decline to exercise it and leave the claims to the arbitrator, particularly where the arbitration is well advanced and the arbitrator has established appropriate procedures. The door remains open for a party to approach the Court at a later stage if circumstances change.
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