The aim of this study is to provide an overview of the different ways to introduce trust management mechanisms in logic-based computing systems (especially multi-agent systems), in order to deal with security problems. This study includes a survey of recent publications in this research area, as well as a critical comparison between them. We try here to put a stress on their common aspects, their differences, the kind of logic paradigm they are based on, and the kind of issues they are likely to address well.