In this paper, the connections reasoning technique (CRT) based on the predication logic is proposed to infer the connections between network nodes. This technique interprets the address forwarding tables (AFTs) as a set of predicate formulas and translates the topology discovery into a mathematic problem of logic reasoning, so that the topology discovery can be studied by resorting to mathematic tools. An algorithm for topology discovery based on CRT is proposed in this paper. Compared with current discovery algorithms, this method excels in: 1) Applying the redundancies in AFTs more effectively, so that the whole topology can be built up by just small part of AFTs; 2) Naturally resolving the problem of topology discovery for multi-subnet switched domain without any extensions. Furthermore, a method with little cost is proposed to discover the dynamic topology in this paper. This algorithm is successfully applied to the network management system for CBISN (Community Broadband Integrated Services Network).