Some results on dyadic deontic logic and the logic of preference

Broadly conceived, deontic logic is the logical study of the normative use of language and its subject matter consists of a variety of normative concepts, notably those of obligation (prescription), prohibition (forbiddance), permission and commitment. A powerful trend of research in the area was initiated by the famous contribution von Wright (1951), where the formal properties of monadic ("unconditional", "absolute") normative concepts were systematically explored. Certain paradoxical results were seen to arise in von Wright's monadic deontic logic, however, which led him to propose systems for dyadic ("conditional", "relative") normative notions, where the concepts of obligation, permission etc., are made relative to, or conditional on certain circumstances. Thus, the dyadic deontic logic of von Wright (1956) was proposed as a reaction to the Prior (1954) Paradoxes of Commitment ("derived obligation"), and that of von Wright (1964) and (1965) as a reaction to the Chisholm (1963) Contrary-to-Duty Imperative Paradox. Our main concern in this paper will be certain later developments of dyadic deontic logic, which are characterized by the endeavor to relate the subject to Preference Theory in some way or other. A preference-theoretical approach to the problems of dyadic deontic logic was proposed by several writers in the late sixties and the early seventies. Pioneering contributions are Sven Danielsson (1968) and Bengt Hansson (1969), followed, e.g., by Bas C. van Fraassen (1972), David Lewis (1974) and Franz von Kutschera (1974). In section 2 below we present the language, syntax, proof-theory and the semantics of an axiomatic system G, which arose as a result of my attempt to reconstruct and to generalize the Hansson (1969) systems of dyadic standard deontic logic; see Aqvist (1984, Chap. VI, §§22-24), G may be said to codify a Hansson-von Kutschera-Aqvist line of interpreting the basic pair O, P of dyadic deontic operators. There is another line of interpreting them, though, which I'd like to call the Danielssonvan Fraassen-Lewis one. From the standpoint of our system G we can