Syncretic Argumentation by means of Lattice Homomorphism and Fusion

The notion of acceptability is a counterpart of the phenomenon observed in our daily argumentation and originates from an old saying, “The one who has the last word laughs best”, as stated by Dung. It is an empirical social truth or wisdom that has been evolved in various cultural sphere over generations and considered useful by people. It is remarkable and suggestive that Dung’s theory of argumentation had started from such a daily but philosophical observation. This might be because argumentation is humans’ most normal but intelligent action for thought and communication by language. There, however, can be a plurality of sets of justified arguments in argumentation as mentioned above, contrasting with the semantics of an ordinary logic that is to be uniquely given by the Tarskian semantics, for example. Naturally, this reflects a figure of argumentation, a decisive difference from a logic. The preferred semantics, for example, is defined as follows