Editing Deontic logic (section)

{{Short description|Field of philosophical logic}}
{{Use dmy dates|date=May 2024}}
'''Deontic logic''' is the field of [[philosophical logic]] that is concerned with [[obligation]], [[permission (philosophy)|permission]], and related concepts.  Alternatively, a deontic logic is a formal system that attempts to capture the essential logical features of these concepts. It can be used to formalize [[imperative logic]], or [[deontic modality|directive modality]] in natural languages. Typically, a deontic logic uses ''OA'' to mean ''it is obligatory that A'' (or ''it ought to be (the case) that A''), and ''PA'' to mean ''it is permitted (or permissible) that A'', which is defined as <math>PA\equiv \neg O\neg A</math>.

In natural language, the statement "You may go to the zoo OR the park" should be understood as <math>Pz\land Pp</math> instead of <math>Pz\lor Pp</math>, as both options are permitted by the statement. When there are multiple agents involved in the [[domain of discourse]], the deontic modal operator can be specified to each agent to express their individual obligations and permissions. For example, by using a subscript <math>O_i</math> for agent <math>a_i</math>, <math>O_iA</math> means that "It is an obligation for agent <math>a_i</math> (to bring it about/make it happen) that <math>A</math>". Note that <math>A</math> could be stated as an action by another agent; One example is "It is an obligation for Adam that Bob doesn't crash the car", which would be represented as <math>O_{Adam}B</math>, where B="Bob doesn't crash the car".