TY - ABST T1 - Adding the Inference Rule Disjunctive Syllogism to Relevant Logics Y1 - 2010 A1 - Lycke, Hans AB -

In order to avoid trivial consequences, the derivability relation of relevant logics (RL) does not support the inference rule disjunctive syllogism (DS). In this paper, I will show that the inference rule DS can be added to this derivability relation in a way that doesn’t lead to trivial or irrelevant consequences. To do so, I will rely on the insights gained from the study of inconsistency–adaptive logics, the branch of adaptive logics that was devised to explicate reasoning based on inconsistent premise sets. Moreover, I will also point to the relations with some alternative proposals from the literature, and I will show that the inconsistency–adaptive framework has some major advantages over these.

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