NEW YORK (CBSNewYork/AP) — A federal judge will decide whether the owners of the World Trade Center can try to make several airlines and other aviation defendants pay billions of dollars in damages from the attacks of Sept. 11, 2001.

Manhattan U.S. District Judge Alvin Hellerstein said he will announce his decision at the end of a bench trial that starts Monday.

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The trial will decide whether World Trade Center Properties and its affiliates, which owned the Twin Towers, can receive more than the $4.9 billion in insurance proceeds they have already gotten.

If the judge rules the trade center owners are entitled to additional money, a liability trial might be scheduled. Hellerstein has already said the maximum the owners could recover from aviation defendants would be $3.5 billion.

The owners said it has cost more than $8 billion to rebuild.

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World Trade Center leaseholder Larry Silverstein has sought to hold American and United Airlines – now United Continental Holdings Inc. – responsible for the 9/11 attacks on the grounds that they failed to provide adequate security, according to an Insurance Journal report.

American Airlines has argued that it is not liable because the hijackings that led to the destruction of the Twin Towers were acts of war, the publication reported.

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