Preference Logic and Its Measurement-Theoretic Semantics

How can we explain why we should ascribe some logical properties to an agent’s preferences, and why we should not ascribe others to them? Although this problem is very important, little attention has been given to it. We break this problem down into the three: Problem 1. When we attempt to ascribe some logical properties to the preferences of an agent, how can we explain this ascription? Problem 2. What logical properties must we ascribe to his preferences if and only if our solution to Problem 1 can be adopted? Problem 3. What logical properties should we ascribe to his preferences and what logical properties should not we ascribe to them? The aim of this paper is to propose a new version of sound and complete preference logic (PL) that can furnish a solution to each of these problems. We solve all of them by providing PL with a Domotor-type semantics that is a kind of measurement-theoretic and decision-theoretic one.