What is the difference between alethic and doxastic logic in formal logic?

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What is the difference between alethic and doxastic logic in formal logic?

In formal logic, alethic logic and doxastic logic are two distinct branches that focus on different aspects of reasoning and belief.

Alethic logic, also known as modal logic, deals with the study of modalities, which are expressions that indicate possibility, necessity, contingency, or impossibility. It examines the relationship between propositions and the truth values associated with them under different modal conditions. Alethic logic aims to analyze and understand concepts such as possibility and necessity, and how they affect the truth or falsity of statements.

On the other hand, doxastic logic, also known as epistemic logic, is concerned with the study of belief and knowledge. It focuses on analyzing and formalizing the concepts of belief, justification, and knowledge, and the relationships between them. Doxastic logic aims to provide a formal framework for reasoning about what an agent believes, what they are justified in believing, and what they know.

In summary, the main difference between alethic and doxastic logic lies in their respective focuses. Alethic logic deals with modalities and the truth values of propositions under different modal conditions, while doxastic logic focuses on belief, justification, and knowledge.