English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

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 propositional-attitude 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 \(\mathcal{S}\), a unique class of algebras \(\mathbb{A}\mathrm{lg}\mathcal{S}\) is canonically associated by the general theory of AAL. We show that for any selfextensional logic \(\mathcal{S}\) such that \(\mathbb{A}\mathrm{lg}\mathcal{S}\) is closed under direct products, any algebra in \(\mathbb{A}\mathrm{lg}\mathcal{S}\) 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.

An Abstract Algebraic Logic View on Judgment Aggregation