A logic of comparative obligation (Q1922824)

Normal systems of modal logic, interpreted as deontic logics, are unsuitable for a logic of conflicting obligations. By using modal operators based on a more complex semantics, however, we can provide for conflicting obligations, as in \textit{B. van Fraassen}'s paper ``Values and the heart's command'' [J. Philos. 70, No. 1, 5-19 (1973)], which is formally similar to a fragment of the logic of ability later given by the author [``The logic of ability'', J. Philos. Log. 17, No. 1, 1-26 (1988; Zbl 0653.03003)]. Having gone that far, we may find it desirable to be able to express and consider claims about the comparative strengths, or degrees of urgency, of the conflicting obligations under which we stand. This paper, building on the formalism of the logic of ability [the author, loc. cit.], provides a complete and decidable system for such a language.