Natural Deduction for Modal Logic of Judgment Aggregation

Abstract

We can formalize judgments as (consistent sets of) logical formulas. Judgment aggregation deals with judgments of several agents, which need to be aggregated to a collective judgment. There are several logical formalizations of judgment aggregation. This paper focuses on a modal formalization which nicely expresses classical properties of judgment aggregation rules and famous results of social choice theory, like Arrow's impossibility theorem. A natural deduction system for modal logic of judgment aggregation is presented in this paper. The system is sound and complete. As an example of derivation, a formal proof of Arrow's impossibility theorem is given.