Measurement-Theoretic Foundation of Preference-Based Dyadic Deontic Logic

Abstract

The contemporary development of deontic logic since von Wright has been based on the study of the analogies between normative and alethic modalities. The weakest deontic logic called standard deontic logic (SDL) is the modal system of type KD. Jones and Sergot argued that contrary-to-duty (CTD) reasoning was necessary to represent the legal codes in legal expert systems. This reasoning invites such CTD paradoxes as Chisholm’s Paradox of SDL that is monadic. Hansson’s dyadic deontic logic can avoid CTD paradoxes. But it introduces such dilemmas as the Considerate Assassin’s Dilemma. Prakken and Sergot, and van der Torre and Tan proposed preference-based dyadic deontic logics that can explain away this dilemma. However, these logics face the Fundamental Problem of Intrinsic Preference. The aim of this paper is to propose a new non-modal logical version of complete and decidable preference-based dyadic deontic logic–conditional expected utility maximiser’s deontic logic (CEUMDL) that can avoid Chisholm’s Paradox and explain away the Considerate Assassin’s Dilemma. In the model of CEUMDL we can explain an agent’s preferences in terms of his degrees of belief and degrees of desire via conditional expected utility maximisation, which can avoid the Fundamental Problem of Intrinsic Preference and furnish a solution to the Gambling Problem. We provide CEUMDL with a Domotor-type model that is a kind of measurement-theoretic and decision-theoretic one.