deontik

Deontik, or deontic modality, is the branch of philosophy and formal logic that concerns normative concepts such as obligation, permission, and prohibition. The term is commonly used to refer to deontic logic, the study of normative statements and the rules that govern them. In formal treatments, deontic operators express what ought to be the case within a system of norms, laws, or rules.

The standard operators are O for obligatory, P for permissible, and F for forbidden. Oφ reads “it is obligatory that φ,” Pφ reads “it is permissible that φ,” and Fφ reads “it is forbidden that φ.” In many logics Fφ is defined as the negation of Pφ, while others treat prohibition as a primitive notion distinct from permission. To handle context-sensitive norms and conditional obligations, some frameworks use dyadic forms such as O(φ|ψ), meaning φ is obligatory given ψ. Dyadic approaches help address problems that arise in monadic deontic logic, such as contrary-to-duty scenarios and related paradoxes.

Historical roots trace to G. H. von Wright in the 1950s, who introduced formal deontic logic. Since then, the field has developed with various systems and refinements, including conditional or dyadic deontic logics and analyses of normative contradictions. These tools are used to model ethical theories, legal norms, contracts, and other normative systems, and to support normative reasoning in artificial intelligence and multi-agent frameworks.

Applications of deontik span philosophy, law, political theory, linguistics, and computer science, where it provides a formal vocabulary for expressing duties, permissions, and prohibitions and for analyzing the implications of normative rules.