Measurement-Theoretic Foundations of Dynamic Epistemic Preference Logic

Abstract

In this chapter, we propose a new version of sound and complete dynamic epistemic preference logic (\({{\mathsf {DEPL}}}\)). Both preference logic and dynamic epistemic logic have gained considerable attention in linguistics, computer science and philosophy. Recently van Benthem and Liu proposed to integrate preference logic with dynamic epistemic logic. They called the resulting logic ‘dynamic epistemic upgrade logic (\({\mathsf {DEUL}}\))’. \({\mathsf {DEUL}}\) is designed only to deal with the dynamic interactions between knowledge and preferences originating from decision makings under certainty. On the other hand, \({{\mathsf {DEPL}}}\) is designed to deal with the dynamic interactions between knowledge and preferences originating from decision makings under certainty, risk, uncertainty and ignorance. So \({{\mathsf {DEPL}}}\) has much wider scope of application than \({\mathsf {DEUL}}\). Providing \({\mathsf {DEPL}}\) with measurement-theoretic semantics enables it to have such wide scope.