deontisch

Deontisch, in philosophy and logic, concerns normative modalities—what ought to be the case, what may be done, and what must not be done. The term is used especially for deontic logic, a formal framework that models obligations, permissions, and prohibitions. In this tradition, statements about duty and right are represented with modal operators attached to propositions. In German-language contexts, deontisch is the standard term for this area of study, which connects logic to law, ethics, and normative theory.

The standard operators are O for obligation (it ought to be that), P for permission (it is permitted that), and F for prohibition (it is forbidden that). Relationships among these notions are often captured by simple definitions, for example P p ≡ ¬F ¬p and F p ≡ ¬P ¬p, though different systems may treat them in other ways. Deontic logic aims to analyze how duties and permissions interact, including how to handle conflicting obligations and exceptions.

Semantics are typically based on possible-world models, sometimes using an ordering of worlds by normative ideality. A sentence O p is true at a world w if p holds in all ideal worlds accessible from w, while P p and F p are defined to reflect permissible and forbidden states across those worlds. This framework supports formal reasoning about legal rules, ethical guidelines, and normative decision-making in complex domains.

History and variants: Deontic logic originated with mid-20th-century work by philosophers such as G. H. von Wright and has since grown into a family of formal systems. Different logics (including SDL and its successors) vary in how they treat contradictions, permissions, and the propagation of duties, reflecting ongoing debates about the proper formalization of normative reasoning.