Judgment aggregation in dynamic logic of propositional assignments

Abstract

Judgment aggregation models a group of agents having to collectively decide over a number of logically interconnected issues starting from their individual opinions. In recent years, a growing literature has focused on the design of logical systems for social choice theory, and for judgment aggregation in particular, making use of logical languages designed ad hoc for this purpose. In this paper we deploy the existing formalism of Dynamic Logic of Propositional Assignments (DL-PA), an instance of Propositional Dynamic Logic where atomic programs affect propositional valuations. We show that DL-PA is a well-suited formalism for modeling the aggregation of binary judgments from multiple agents, by providing logical equivalences in DL-PA for some of the best-known aggregation procedures, desirable axioms coming from the literature on judgment aggregation and properties for the safety of the agenda problem.

Resource separation in dynamic logic of propositional assignments

“…Dynamic Logic of Propositional Assignments DL-PA [BHT13,BHST14] is a version of Propositional Dynamic Logic PDL whose atomic programs are assignments of propositional variables p to true or false, respectively written +p and −p. We and coauthors have shown that many knowledge representation concepts and formalisms can be captured in DL-PA, such as update and revision operations [Her14], database base fusion and repair operations [FHR19], planning [HMNDBW14,HMV19], lightweight dynamic epistemic logics [CS15,CHM + 16,CS17], and judgment aggregation [NGH18]. The mathematical properties of DL-PA are simpler than those of PDL, in particular, the Kleene star can be eliminated [BHT13] and satisfiability and model checking are both PSPACE complete [BHST14].…”

Resource Separation in Dynamic Logic of Propositional Assignments

“…Dynamic Logic of Propositional Assignments DL-PA [BHT13,BHST14] is a version of Propositional Dynamic Logic (PDL) whose atomic programs are assignments of propositional variables p to true or false, respectively written +p and −p. We and coauthors have shown that many knowledge representation concepts and formalisms can be captured in DL-PA, such as update and revision operations [Her14], database repair [FHR19], lightweight dynamic epistemic logics [CS15,CHM + 16,CS17], planning [HMNDBW14], and judgment aggregation [NGH18]. The mathematical properties of DL-PA are simpler than those of PDL, in particular, the Kleene star can be eliminated [BHT13] and satisfiability and model checking are both PSPACE complete [BHST14].…”