Abstract There are not very many existing logics of belief which have both a perspicuous semantics and are computationally attractive. An exception is the logic SL, proposed by Liu, Lakemeyer, and Levesque, which allows for a decidable and often even tractable form of reasoning. While the language is first-order and hence quite expressive, it still has a number of shortcomings. For one, beliefs about beliefs are not addressed at all. For another, the names of individuals are rigid, that is, their identity is assumed to be known. In this paper, we show how both shortcomings can be overcome by suitably extending the language and its semantics. Among other things, we show that determining the beliefs of a certain kind of fully introspective knowledge bases is decidable and that unknown individuals in the knowledge base can be accommodated in a decidable manner as well.