Mathematics Stack Exchange
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Questions tagged [modal-logic]

Questions relating to deductions relating to the expressions "it is necessary that" and "it is possible that"

Modal logic is an extension of propositional and predicate logic that expresses modalities, which are qualifications to a statement. The most commonly used modalities in mathematics are "possibly," "necessary," and "impossibly."

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Validity at state w

Book called 'Modal Logic' has an definition for validity in page 125. It says in the first part: "A formula $\phi$ is valid at a state w in a frame F if $\phi$ is true at w in every model (F,V) based on F". And the notion is $F,w\models \phi $ I did…
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Equivalent formulations of the axiom K in modal logic

In modal logic, the axiom K can be equivalently formulated as: (1) $\Box(p\rightarrow q)\rightarrow (\Box p\rightarrow\Box q)$ (2) $\Box(p\wedge q)\leftrightarrow (\Box p\wedge\Box q)$ (3) $\Diamond(p\vee q)\leftrightarrow (\Diamond p\vee\Diamond…
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