Soft Deontic Logic

Abstract

Deontic logic is the theory of valid inference rules containing qualifications of prohibition, duty, or permission. Three main assumptions of standard deontic-logic approaches are here discussed and rejected: (1) the modal conception of deontic logic, according to which «licit» means «possible without breaking the rules»; (2) the gap between facts and norms, which contends that what actually happens has no bearing on duties; and (3) bivalence, which bars any situation inbetween absolute truth and downright falseness. As against such approaches, we put forward an alternative deontic logic we call soft, which, while being fuzzy (and based on a a paraconsistent gradualistic sentential calculus), binds duties to facts by espousing the implantation principle, according to which, if A is the case, then the duty (or permission) to do B-if-A implies the duty (or permission) to do B. By embracing degrees of licitness our proposal upholds a principle of proportionality ruling out deontic leaps. A formalized axiomatic system along those lines is developed.