This paper provides a logically precise analysis of agreement and disputes in dialogue. The semantics distinguishes among the public commitments of each dialogue agent, including commitments to relational speech acts or rhetorical relations (e.g. Narration, Explanation and Correction). Agreement is defined to be the shared entailments of the agents' public commitments. We show that this makes precise predictions about implicit agreement. The theory also provides a consistent interpretation of disputes and models what content is agreed upon when a dispute has taken place.