Judgment aggregation in dynamic logic of propositional assignments

Arianna Novaro (1) , Umberto Grandi (1, 2) , Andreas Herzig (1, 3)

1 IRIT-LILaC - Logique, Interaction, Langue et Calcul
2 UT Capitole - Université Toulouse Capitole
3 CNRS - Centre National de la Recherche Scientifique

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.

Mots clés: DL-PA; Dynamic Logic of Propositional Assignments; Dynamic Logic; Modal Logic; Social Choice Theory; Computational Social Choice; Automated Reasoning

Domaines: Logique en informatique [cs.LO]

Arianna Novaro, Umberto Grandi, Andreas Herzig. Judgment aggregation in dynamic logic of propositional assignments. Journal of Logic and Computation, 2018, 28 (7), pp.1471-1498. ⟨10.1093/logcom/exy024⟩. ⟨hal-02089335v2⟩