Formalizing reasoning for compromise toward dialectical conflict resolution

Argumentation in artificial intelligence, often called computational dialectics, is rooted in Aristotle's idea of evaluating argumentation in a dialogue model. In contrast, Chinese traditional philosophy regards dialectics as a style of reasoning that focuses on contradictions and how to resolve them, transcend them or find the truth in both. A compromise is considered one way to resolve conflicts dialectically. In this paper, we formalize reasoning intended to derive a compromise. Both the reasoning and the compromise are defined on abstract lattices procedurally and declaratively, respectively. We prove that the reasoning is sound and complete with respect to the compromise. Then we define the concrete and sound algorithm for the reasoning on the lattice characterized by definite clausal language and generalized subsumption. Under some conditions, the reasoning offers a unified way to reason rationally whether a set of the premises is consistent or not. Such reasoning is outside the scope of logics that have the principle of explosion. Further, the compromise has a unique logical setting compared with other types of reasoning such as deduction, induction, and abduction. We incorporate the reasoning into arguments, and illustrate that the use of arguments with compromise contributes to realizing a compromise-based conflict resolution in argumentation.