Car company Group Lotus and F1's Team Lotus are at loggerheads over the name.
Team Lotus chief executive officer Riad Asmat dismisses Group Lotus's reasons for terminating the contract as "trivial".
Last year, Mr Fernandes' team raced as Team Lotus - a name that was not owned by Group Lotus.
In 2010, Mr Fernandes revived the Lotus brand in Formula 1 racing, having obtained a licence from Group Lotus to race as Lotus Racing.
Fernandes, the boss of the Air Asia airline, is also suing Group Lotus for breach of contract over its decision to terminate the licence agreement.
Group Lotus - part of Malaysia's Proton car company - is sponsoring the Renault team this season and the Russian sports car manufacturer Marussia has bought into Virgin.
Monday's hearing surrounded Group Lotus's decision to terminate a five-year licensing deal it had with Team Lotus boss Tony Fernandes's 1Malaysia group to use the Lotus brand in F1.
Fernandes bought the rights to the Team Lotus name in an attempt to protect his investment in F1 when he realised he had fallen out of favour at Group Lotus.
Renault no longer has its own Formula 1 team, though its Renault Sport F1 division supplies engines to Caterham as well as to the Lotus F1 team, which is run by Group Lotus.
In the course of 2009, Group Lotus appointed a new chief executive officer, Dany Bahar, who last year decided that the company would be better represented in F1 by sponsoring a more established team.
The row dates back to 2009, when Fernandes was granted by Group Lotus the rights to use the Lotus name in F1 for a new team he was setting up to race in the 2010 season.
Group Lotus had applied for a summary judgement - where a judge decides a case there and then and stops it going to a full trial - that it was within its rights to end its relationship with Fernandes and that he had no rights to use the Lotus name.
The programs, an addition to the company's "Lotus" group of applications, also represent one of IBM's most ambitious forays yet into enterprise software-as-a-service, the browser-based model of applications pioneered by companies like Salesforce.com.
Carl Tyler, a veteran of Lotus and IBM who now runs Instant Technologies, an enterprise IM software group, thinks one of the biggest etiquette breaches by Gen Y recruits involves newbies typing paragraph upon paragraph of chat.
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