Peer review is a cornerstone of the academic editorial decisionmaking process, yet it faces significant challenges. Artificial intelligence can help address these challenges, but its use raises concerns about reliability and the potential for reproducing existing biases. In this research, we employ a formal argumentation-Theoretic framework that allows for explicit analysis of arguments and their interrelations, combined with argument mining techniques to streamline the formalization of peer reviews, and resulting in a neuro-symbolic approach to dispute resolution. Our method involves identifying parties arguments in peer reviews and representing them as abstract argumentation frameworks, which facilitate dispute resolution through logical inference. We annotate these frameworks within a corpus of scientific peer reviews, achieving a high Krippendorff s alpha of 0.81. Having the annotated corpus, we implement an argument mining pipeline that integrates BERT sentence embeddings with an LSTM model, classifying sentences into three categories: Authors arguments, reviewers arguments, and nonarguments. We achieved an accuracy of 0.634 and an F1 score of 0.631, which are comparable to models trained on other datasets. However, our approach stands out by enabling the processing of the extracted argumentation with logical inference.