Міндет, рұқсат және логиканың философиялық аспектілері

Field of philosophical logic
Deontic logic is the field of philosophical logic that is concerned with obligation, 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 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
Note that in natural language, the statement "You may go to the zoo OR the park" should be understood as instead of , as both options are permitted by the statement; See Hans Kamp's paradox of free choice for more details. 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 for agent , means that "It is an obligation for agent (to bring it about/make it happen) that ". Note that 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 , where B="Bob doesn't crash the car".

The term deontic is derived from the δέον (gen.: δέοντος), meaning "that which is binding or proper."

The accessibility relation between possible world is interpreted as acceptability relations: is an acceptable world (viz. ) if and only if all the obligations in are fulfilled in (viz. ).

Alan R. Anderson (1959) shows how to define in terms of the alethic operator and a deontic constant (i. e. 0 ary modal operator) standing for some sanction (i. e. bad thing, prohibition, etc. ): Intuitively, the right side of the biconditional says that A's failing to hold necessarily (or strictly) implies a sanction. In addition to the usual modal axioms (necessitation rule N and distribution axiom K) for the alethic operator , Anderson's deontic logic only requires one additional axiom for the deontic constant : , which means that there is alethically possible to fulfill all obligations and avoid the sanction. This version of the Anderson's deontic logic is equivalent to SDL. However, when modal axiom T is included for the alethic operator , it can be proved in Anderson's deontic logic that , which is not included in SDL. Anderson's deontic logic inevitably couples the deontic operator with the alethic operator , which can be problematic in certain cases.

Many other varieties of deontic logic have been developed, including non monotonic deontic logics, paraconsistent deontic logics, and dynamic deontic logics.

Philosophers from the Indian Mimamsa school to those of Ancient Greece have remarked on the formal logical relations of deontic concepts and philosophers from the late Middle Ages compared deontic concepts with alethic ones. In his Elementa juris naturalis (written between 1669 and 1671), Gottfried Wilhelm Leibniz notes the logical relations between the licitum (permitted), the illicitum (prohibited), the debitum (obligatory), and the indifferens (facultative) are equivalent to those between the possibile, the impossibile, the necessarium, and the contingens respectively.