Extensionality for obligations in Åqvist’s system F

Abstract

The dyadic deontic logic system F is one of the best known preference-based deontic logics. It was introduced as a propositional logic, by Lennart Åqvist to offer a solution to contrary-to-duty paradoxes plaguing the field of deontic logic. This thesis addressed the challenging topic of extending the system F to first-order. We construct a first-order dyadic deontic logic system extending propositional F, which includes equality and definite descriptions in its language and an extensional dyadic deontic operator. To better understand equality, definite descriptions and extensional operators and why we want our system to include them, we investigate them in detail. We show which characterising properties a logic system has to fulfil to express those notions meaningfully and accurately. Furthermore, we demonstrate which problems must be circumvented when defining such a system. We provide two different first-order dyadic deontic logic systems extending the propositional system F. For each of them we introduce semantics, using Kripke models, and a Hilbert calculus. Moreover, we show that the Hilbert axiomatisations are sound in their respective semantics, that is if there is a derivation of a formula Phi in the calculus from a set of premises Gamma, then Phi is a semantical consequence of Gamma.