The case is being heard by the Royal Courts of Justice sitting in Belfast
The British Supreme Court has started hearing an appeal in Belfast involving a refusal by a Christian-owned bakery to create a cake for a gay rights group.
A lower court previously ruled the decision not to bake the cake, iced with the slogan 'Support Gay Marriage', was discriminatory.
Ashers Bakery refused to bake the cake with the pro-gay marriage slogan on it in 2014 and was fined stg£500 (€700).
Gareth Lee had asked the bakery to ice a cake depicting 'Sesame Street' characters Bert and Ernie and the logo for the campaign group, Queerspace.
Northern Ireland's publicly funded Equality Commission brought a civil action, alleging that the bakery breached its statutory duty not to discriminate on the grounds of sexual orientation.
A court ruled Mr Lee was discriminated against on the grounds of sexual orientation.
The bakery appealed the ruling, which was dismissed in October 2016.
Daniel McArthur claims his family have come under attack for exercising their basic right to live according to their beliefs.
Michael Wardlow is from the Equality Commission in Northern Ireland.
"That Christian belief once it moves into the public realm - remembering they're a limited company, they're not just individuals - a company limited by guarantee.
"They choose to trade in a public realm, receive money and therefore they are subject to the laws.
"The laws are adequately struck between that balance at the moment".
The Supreme Court has listed a two-day hearing for legal arguments May 1st and 2nd at the Royal Courts of Justice in Belfast.