Deontic logic primarily investigates the nature of moral values, obligations, permissions, and prohibitions, and how they relate to human actions and decision-making.

A deontic statement expresses a moral obligation, permission, or prohibition. In this case, "You should tell the truth" conveys a moral obligation to be honest.

An obligation is a moral requirement that must be fulfilled, while a permission is a moral allowance that grants the freedom to act or not act in a certain way.

In deontic logic, the implication operator (→) is often used to represent obligation. For example, the statement "It is obligatory to tell the truth" can be expressed as "Truth-telling → Obligation".

In deontic logic, an obligation to perform an action implies the permission to perform that action, but the converse is not necessarily true. For example, if it is obligatory to tell the truth, then it is also permissible to tell the truth, but the permission to tell the truth does not imply an obligation to do so.

A conflict between obligations arises when an individual is faced with two or more obligations that cannot be simultaneously fulfilled. In the case of a doctor and a soldier, their respective obligations may conflict in situations where saving lives requires actions that compromise national defense or vice versa.

The primary purpose of a deontic logic system is to provide a formal framework for analyzing and evaluating moral reasoning. It aims to clarify the logical relationships between moral concepts and principles, and to identify and resolve inconsistencies or conflicts in moral judgments.

Georg Henrik von Wright is generally regarded as the founder of modern deontic logic. His seminal work, "An Essay in Deontic Logic," published in 1951, laid the groundwork for the formal study of obligation, permission, and prohibition in a logical framework.

In deontic logic, a strong obligation is a moral requirement that must be fulfilled, while a weak obligation is a moral requirement that is permissible to fulfill but not necessarily required. A strong obligation is often associated with moral necessity, while a weak obligation is associated with moral permissibility.

In deontic logic, the disjunction operator (∨) is often used to represent permission. For example, the statement "It is permissible to tell the truth" can be expressed as "Truth-telling ∨ Permission".

In deontic logic, permission and prohibition are generally considered to be mutually exclusive. If an action is permitted, then it is not prohibited, and vice versa. This relationship ensures that there is no logical contradiction between allowing and forbidding the same action.

A conflict between permissions arises when an individual is granted two or more permissions that cannot be simultaneously exercised. In the case of the student, they cannot both attend the party and stay home to study at the same time.

The purpose of a deontic logic system in relation to moral decision-making is to provide a framework for analyzing and evaluating moral choices. It offers a structured approach to examining the logical relationships between moral concepts, principles, and obligations, helping individuals to reason about and make informed moral decisions.

David Hume is known for his influential work on deontic logic and the concept of supererogation. In his "Treatise of Human Nature," Hume argued that moral obligations are not derived from reason alone but rather from sentiments and emotions. He also introduced the concept of supererogation, which refers to actions that go beyond what is morally required but are still considered praiseworthy.

In deontic logic, a prohibition is a moral requirement to refrain from performing a specific action, while a negative obligation is a moral requirement to refrain from performing a general type of action. Prohibitions are often expressed using the phrase "It is forbidden to," while negative obligations are expressed using the phrase "It is obligatory not to."