An abstract algebraic logic view on judgment aggregation

María Esteban, Alessandra Palmigiano, Zhiguang Zhao

Research output: Chapter in Book / Report / Conference proceedingConference contributionAcademicpeer-review

Abstract

In the present paper, we propose Abstract Algebraic Logic (AAL) as a general logical framework for Judgment Aggregation. Our main contribution is a generalization of Herzberg’s algebraic approach to characterization results on judgment aggregation and propositionalattitude aggregation, characterizing certain Arrovian classes of aggregators as Boolean algebra and MV-algebra homomorphisms, respectively. The characterization result of the present paper applies to agendas of formulas of an arbitrary selfextensional logic. This notion comes from AAL, and encompasses a vast class of logics, of which classical, intuitionistic, modal, many-valued and relevance logics are special cases. To each selfextensional logic S, a unique class of algebras AlgS is canonically associated by the general theory of AAL. We show that for any selfextensional logic S such that AlgS is closed under direct products, any algebra in AlgS can be taken as the set of truth values on which an aggregation problem can be formulated. In this way, judgment aggregation on agendas formalized in classical, intuitionistic, modal, many-valued and relevance logic can be uniformly captured as special cases. This paves the way to the systematic study of a wide array of “realistic agendas” made up of complex formulas, the propositional connectives of which are interpreted in ways which depart from their classical interpretation. This is particularly interesting given that, as observed by Dietrich, nonclassical (subjunctive) interpretation of logical connectives can provide a strategy for escaping impossibility results.

Original languageEnglish
Title of host publicationLogic, Rationality, and Interaction - 5th International Workshop, LORI 2015, Proceedings
EditorsWen-Fang Wang, Wiebe van der Hoek, Wesley H. Holliday
PublisherSpringer Verlag
Pages77-89
Number of pages13
ISBN (Print)9783662485606
DOIs
Publication statusPublished - 1 Jan 2015
Externally publishedYes
Event5th International Workshop on Logic, Rationality, and Interaction, LORI 2015 - Taipei, Taiwan, Province of China
Duration: 28 Oct 201531 Oct 2015

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume9394
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference5th International Workshop on Logic, Rationality, and Interaction, LORI 2015
CountryTaiwan, Province of China
CityTaipei
Period28/10/1531/10/15

Keywords

  • Abstract algebraic logic
  • Algebra homomorphism
  • Impossibility theorems
  • Judgment aggregation
  • Logical filter
  • Systematicity

Fingerprint

Dive into the research topics of 'An abstract algebraic logic view on judgment aggregation'. Together they form a unique fingerprint.

Cite this