Multiplex semantics for deontic logic (Q2718311)

By a multiplex semantics for deontic logic the author means a possible-worlds semantics with multiple accessibility relations. His purpose is to use this multiplicity in order to handle problems of conflicting obligation. Specifically, he defines one-place deontic operators representing upper and lower obligation, and two-place operators expressing relative weight of obligation.NEWLINENEWLINENEWLINEUpper obligation treats a proposition as obligatory (in a world) iff it is so under at least one of the accessibility relations of the model. Likewise, lower obligation requires the proposition to be obligatory under all of the accessibility relations of the model. The two-place connective \(A\leq B\) of relative weight of obligation is evaluated by ranking the family of accessibility relations of the model, and requiring that for every relation \(R\) in the model rendering \(A\) obligatory (at a given world) there is a relation \(R'\) of the model, at least as highly ranked as \(R\), that renders \(B\) obligatory (in the same world).NEWLINENEWLINENEWLINEThe formal properties are studied in detail, with completeness theorems for appropriate axiomatizations.