Judgment Aggregation in Dynamic Logic of Propositional Assignments
Arianna Novaro
Abstract:
Judgment Aggregation studies how agents take a collective decision on a certain number of issues based on their individual opinions. In recent years, a line of research in Judgment Aggregation investigates how to model this framework within a logical calculus — usually designed ad hoc for this purpose. By contrast, in this thesis we show how it is possible to translate any aggregation problem formulated in Binary Aggregation with Integrity Constraints (a model for Judgment Aggregation) into Dynamic Logic of Propositional Assignments (an instance of Propositional Dynamic Logic). In the first part of our work, we show how to appropriately express many well-known aggregation procedures as programs. Then, we translate some desirable properties of aggregation rules, i.e. axioms, as formulas of the logic. Finally, we connect the work carried out in the previous parts to model results about a problem known as the safety of the agenda. The positive outcome of our approach thus suggests this to be a promising path for future investigation, both as a means to formally express other areas of Judgment Aggregation, and as opening the way towards the use of automated reasoning techniques in this field.