Ontology alignments enable agents to communicate while preserving heterogeneity in their knowledge. Alignments may not be provided as input and should be able to evolve when communication fails or when new information contradicting the alignment is acquired. The Alignment Repair Game (ARG) has been proposed for agents to simultaneously communicate and repair their alignments through adaptation operators when communication failures occur. ARG has been evaluated experimentally and the experiments showed that agents converge towards successful communication and improve their alignments. However, whether the adaptation operators are formally correct, complete or redundant could not be established by experiments. We introduce a logical model, Dynamic Epistemic Ontology Logic (DEOL), that enables us to answer these questions. This framework allows us (1) to express the ontologies and alignments used via a faithful translation from ARG to DEOL, (2) to model the ARG adaptation operators as dynamic modalities and (3) to formally define and establish the correctness, partial redundancy and incompleteness of the adaptation operators in ARG.