Market Basket CEO Arthur T. Demoulas and the Massachusetts-based company's board of directors agree on one thing after publicly feuding for months: They're both hoping mediation talks that start today lead to a "successful" resolution of the supermarket chain's internal fight.

The closed-door talks are happening in Delaware, where the company is incorporated. Demoulas, who was suspended by the board in May, will take part in the proceedings.

"Mr. Demoulas firmly believes that mediation represents the best path to resolution of the issues facing Market Basket and is committed to reaching agreement," Demoulas spokesperson Justine Griffin said in a statement. "He is confident that if the board shares that commitment, mediation will be successful."

Harvey Wolkoff, an attorney for th

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