Logics for Collective Reasoning

In this paper, we discuss the approach based on Social Choice Theory and Judgment Aggregation to the definition of collective reasoning. We shall make explicit the aggregative nature of the notion of collective reasoning that is defined in the Judgment Aggregation account and we shall stress that the notion of logical coherence plays a fundamental role in defining collective attitudes. Unfortunately, as several results in Judgment Aggregation show, coherence is not compatible with fair aggregation procedures. On closer inspection, the notion of coherence that is jeopardized by Judgment Aggregation is based on classical logic. In this work, we propose to revise the standard view of rationality of Judgment Aggregation by exploring the realm of non-classical logics. in particular, we will present possibility results for substructural logics. Those logics, we argue, provide a viable notion of collective reasoning.