Deontic logic
Deontic logic is a branch of modal logic that deals with concepts of obligation, permission, and prohibition. It explores the logical relationships between statements about what is obligatory, permissible, or forbidden, often in the context of ethics, law, or social norms. In essence, it provides a formal framework for reasoning about what ought to be, rather than what is.
Core Concepts:
- Obligation: What one must do or what is required.
- Permission: What one is allowed to do.
- Prohibition: What one is forbidden from doing.
Formal Representation:
- Deontic logic uses modal operators to represent these concepts. For example, “O” might represent “it is obligatory that,” and “P” might represent “it is permitted that”.
- So, “O(p)” would mean “it is obligatory that p,” and “P(q)” would mean “it is permitted that q”.
Key Aspects:
- Standard Deontic Logic (SDL): The most commonly used system of deontic logic, building on classical propositional logic and modal logic.
- Mally’s Deontic Logic: An early system of deontic logic, developed by Ernst Mally, which faced certain technical challenges.
- Conditional Obligations: Deontic logic also deals with obligations that depend on certain conditions, like “if it is raining, then it is obligatory to take an umbrella”.
- Paradoxes and Problems: Deontic logic has faced various challenges and paradoxes, leading to refinements and extensions of the basic systems.
- Applications: Deontic logic has applications in various fields, including ethics, law, computer science, and artificial intelligence.
In essence, deontic logic provides a formal language and system for reasoning about norms and obligations, helping us understand the logical structure of moral and legal reasoning, as well as other systems of rules and regulations,.
AI responses may include mistakes.
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[4] https://mally.stanford.edu/deontic.html
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[9] wikipedia/en/Deontic_logic
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[16] https://www.gjclokhorst.nl/lokhorst_1996_studia_logica.pdf
[17] https://philarchive.org/archive/MCNDL-3
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