ABSTRACT
In the present test of our theory we investigate the conceptual domain of “deontic” modalities, which concerns the logic of obligation. The central notions to be formalized are obligation, permissibility, and commitment (or derived obligation). Our proposed deduction model, Md, is inspired by von Wright’s (1964, 1965) system of dyadic deontic modalities. Von Wright’s system was designed particularly to formalize commitment, that is, the logic of such sentences as “if a person borrows money then he ought to repay.” Although this sentence seems straightforwardly to be a conditional of the form p → Oq (where O means “it is obligatory that”), such a representation of commitment quickly leads to counterintuitive results in the presence of certain plausible axioms of deontic logic. The same is true for representing commitment by formulas of the form O(p → q). Føllesdal and Hilpinen (1970) review the matter. In the face of these results, von Wright proposed dyadic formulas like Opq as a formalization of commitment and related concepts. Opq may be read “p is obligatory under circumstances q,” where p is an act and q is a proposition, von Wright’s system is not satisfactory in all respects; see Føllesdal and Hilpinen (1970) for discussion. Nonetheless, his basic idea of dyadic formulas as a representation of commitment and kindred notions appears to be sound, and we shall employ it in our deduction model. To this we now turn.
