Interaction between species in microbial communities plays an important role in the functioning of all ecosystems, from cropland soils to human gut microbiota. Many statistical approaches have been proposed to infer these interactions from microbial abundance information. However, these statistical approaches have no general mechanisms for incorporating existing ecological knowledge in the inference process. We propose an Abductive/Inductive Logic Programming (A/ILP) framework to infer microbial interactions from microbial abundance data, by including logical descriptions of different types of interaction as background knowledge in the learning. This framework also includes a new mechanism for estimating the probability of each interaction based on the frequency and compression of hypotheses computed during the abduction process. This is then used to identify real interactions using a bootstrapping, re-sampling procedure. We evaluate our proposed framework on simulated data previously used to benchmark statistical interaction inference tools. Our approach has comparable accuracy to SparCC, which is one of the state-of-the-art statistical interaction inference algorithms, but with the the advantage of including ecological background knowledge. Our proposed framework opens up the opportunity of inferring ecological interaction information from diverse ecosystems that currently cannot be studied using other methods.