In the course of dialogues such as negotiations about what to do, agents take turns to exchange propositions, starting from some initial disagreement and aiming at agreement. It is claimed that propositions are often associated with personal values. An agent’s underlying purpose in the dialogue is to see to it that the agreement best satisfies their values, leading to a course of action that is in some sense consistent with them. However, in the literature, the relationships between propositions and values is often not transparent. In the Value-based Formal Reasoning model, these relationships are formalised. However, as an abstract model, it rather strict. It would seem that a more lenient and flexible model is called for, particularly with the aim of attaining agreement amongst agents. This flexible model enables agents to, in effect, “trade off” propositions that are associated with less important values for those that are more important. This paper contributes a formal representation of values in a set-theoretic lattice and associates sets of values with sets of propositions. It provides a formal mechanism to represent negotiation, wherein agents can achieve a maximally satisfying result relative to their particular sets of values. The proposal allows agents to agree on propositions, yet disagree on values.