Reasoning about hierarchical structures, where a simple inheritance could be complicated by possible exceptions, is an interesting research topic in artificial intelligence. The fundamental problems in this area are of a formal nature and they are solved using proper formalization. In this paper semantic networks with default and exception links are considered as a basic formalization. Of course, a formalization in a standard logic should be useful because of the clear semantics and well- developed proof methods. The main ambition of the authors is to show that linear logic offers means to represent semantic networks. The paper begins with some examples in graph form of what is expected of semantic networks. Then some definitions connected to taxonomic networks with exceptions (TNE) are given. The kernel of the paper is devoted to the fragment of linear logic in which TNE can be axiomatized. With a TNE a taxonomic linear theory is associated. An alternative -- and a more standard -- way how to represent TNE is based on default logic. A taxonomic default theory associated with TNE is defined. The main result of the paper is a theorem stating a kind of equivalence between taxonomic default theory \(({\mathcal D} ({\mathcal N}))\) and taxonomic linear theory \(({\mathcal T} ({\mathcal N}))\), both associated to a given TNE. (In more technical terms, an exact correspondence between simple sequents provable in \({\mathcal T} ({\mathcal N})\) and extensions of \({\mathcal D} ({\mathcal N})\) is proved).