Judgment aggregation in non-classical logics

TL;DR

This paper explores how judgment aggregation behaves within various non-classical logics, adapting the standard framework to these weaker systems to examine the persistence of classical impossibility results.

Contribution

It adapts judgment aggregation theory to non-classical logics like Intuitionistic Logic and Linear Logic, analyzing the impact on known impossibility results.

Findings

Impossibility results may not hold in certain non-classical logics.

Non-classical logics provide alternative modeling options for agents' reasoning.

Framework adaptation enables analysis of judgment aggregation beyond classical logic.

Abstract

This work contributes to the theory of judgment aggregation by discussing a number of significant non-classical logics. After adapting the standard framework of judgment aggregation to cope with non-classical logics, we discuss in particular results for the case of Intuitionistic Logic, the Lambek calculus, Linear Logic and Relevant Logics. The motivation for studying judgment aggregation in non-classical logics is that they offer a number of modelling choices to represent agents' reasoning in aggregation problems. By studying judgment aggregation in logics that are weaker than classical logic, we investigate whether some well-known impossibility results, that were tailored for classical logic, still apply to those weak systems.