A Deontic Logic with Temporal Qualification

Abstract

There are more than enough various (syntactical, semantical, pragmatical) difficulties in constructing deontic logic. We suppose that at least some of them can be overcome by means of the temporal qualification of the relation of deontic alternativeness and by modification of the so-called “standard” models. We use a temporal structure that is discrete, branching “to the left” and infinite in both directions. The system of tense-logic based on this structure has been developed thanks to works by J.P.Burgess. The essence of our development consists of providing the system with facilities for comparing the times of events found on different “branches” of a set of possible courses of events. Our addition to the Burgess system consists of the axioms of discreteness and of axioms that circumscribe characteristics of the special operator “It is necessary that at the appointed time (so to speak ‘in its own term’) it will be the case that some state of affairs is obtained”. For the constructed system proofs of its soundness, adequacy, and thus, completeness have been obtained. There is also the proof of its decidedness. Now it is possible to attach quite natural temporal interpretation to deontic operators and to introduce into the language used special modal-temporal operators. Completeness and decidedness of the tensed logical system apply to a system of deontic logic with above-mentioned modalities.