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We extend the epistemic logic with De Morgan negation by Fagin et al. (Artif.Intell. 79, 203-240, 1995) by adding operators for universal and commonknowledge in a group of agents, and with a formalization of information updateusing a generalized version of the left division connective of thenon-associative Lambek calculus. We provide sound and complete axiomatizationsof the basic logic with the group operators and the basic logic with groupoperators and updates. Both logics are shown to be decidable.

First Degree Entailment with Group Attitudes and Information Updates