Which deontic modality expresses a moral or legal requirement to perform an action?

Which deontic modality grants the freedom to perform or refrain from an action without any moral or legal constraints?

Which deontic modality strictly forbids an action and imposes a moral or legal duty to refrain from performing it?

In deontic logic, the symbol 'O' is commonly used to represent which deontic modality?

Which deontic modality is often expressed using the phrase 'it is permissible to'?

In deontic logic, the symbol 'F' is commonly used to represent which deontic modality?

Which deontic modality is often expressed using the phrase 'it is forbidden to'?

In deontic logic, the relationship between obligation and permission is often represented using the following formula: $O(p) ≡ ¬F(¬p)$. What does this formula express?

Which deontic modality is often expressed using the phrase 'it is morally required to'?

In deontic logic, the relationship between permission and prohibition is often represented using the following formula: $P(p) ≡ ¬O(¬p)$. What does this formula express?

Which deontic modality is often expressed using the phrase 'it is legally prohibited to'?

In deontic logic, the relationship between obligation and prohibition is often represented using the following formula: $O(p) ∨ P(¬p)$. What does this formula express?

Which deontic modality is often expressed using the phrase 'it is morally permissible to'?

In deontic logic, the relationship between permission and obligation is often represented using the following formula: $P(p) ⊃ ¬O(¬p)$. What does this formula express?

Which deontic modality is often expressed using the phrase 'it is legally required to'?