In this paper, we present an approach for extending the existing concept of nanopublications --- tiny entities of scientific results in RDF representation --- to broaden their application range. The proposed extension uses English sentences to represent informal and underspecified scientific claims. These sentences follow a syntactic and semantic scheme that we call AIDA (Atomic, Independent, Declarative, Absolute), which provides a uniform and succinct representation of scientific assertions. Such AIDA nanopublications are compatible with the existing nanopublication concept and enjoy most of its advantages such as information sharing, interlinking of scientific findings, and detailed attribution, while being more flexible and applicable to a much wider range of scientific results. We show that users are able to create AIDA sentences for given scientific results quickly and at high quality, and that it is feasible to automatically extract and interlink AIDA nanopublications from existing unstructured data sources. To demonstrate our approach, a web-based interface is introduced, which also exemplifies the use of nanopublications for non-scientific content, including meta-nanopublications that describe other nanopublications.