Story highlights Bobby James Moore was convicted of the 1980 murder of an employee at a Houston supermarket

Supporters of Moore hope the court's eventual ruling will bring Texas in line with precedent

Washington (CNN) Five Supreme Court justices Tuesday seemed to agree with arguments that a Texas death row inmate should not be executed because he is intellectually disabled.

The challenge to the Texas death sentence is an opportunity for the court to further define standards states may use in determining intellectual disability. Justices have previously ruled that the execution of the intellectually disabled violates the Constitution, but the court has largely left it up to the states to implement the ruling.

Tuesday, the four liberal justices -- joined critically by Justice Anthony Kennedy -- seemed to indicate that a Texas court had relied upon the wrong standards in ruling against the inmate, Bobby James Moore.

A lawyer for Moore argued that Texas had "adopted a unique approach" and urged the Supreme Court to reverse the decision.

Supporters of Moore hope that the court's eventual ruling will bring Texas -- a state that has executed more people than any other state since 1976 -- in line with Supreme Court precedent.

Read More