A neurocomputational model based on emergent massively overlapping neural cell assemblies (CAs) for resolving prepositional phrase (PP) attachment ambiguity is described. PP attachment ambiguity is a well-studied task in natural language processing and is a case where semantics is used to determine the syntactic structure. A large network of biologically plausible fatiguing leaky integrate-and-fire neurons is trained with semantic hierarchies (obtained from WordNet) on sentences with PP attachment ambiguity extracted from the Penn Treebank corpus. During training, overlapping CAs representing semantic similarities between the component words of the ambiguous sentences emerge and then act as categorizers for novel input. The resulting average resolution accuracy of 84.56% is on par with known machine learning algorithms.