The syntax of autoepistemic logic uses a modal operator that allows us to distinguish between what is true and what is believed.
12.
For compliance with Common Logic, such formulae can be treated as irregular expressions, with the necessity modal operator treated as an uninterpreted symbol.
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Modal logics include additional modal operators, such as an operator which states that a particular formula is not only true, but necessarily true.
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Alternative symbols used for the modal operators are " L " for " Necessarily " and " M " for " Possibly ".
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For each modal operator, one needs to transition from a world in the model to a world that is accessible through the accessibility relation.
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The first results by adding an alethic modal operator \ Box in order to express the Kantian claim that " ought implies can ":
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A logic with infinitely many modalities is ( propositional ) dynamic logic, introduced in 1976 and having a separate modal operator for every regular expression.
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This law is shown to fail in general in at least two cases : ( i ) when t is irreferential and ( ii ) when Q contains modal operators.
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In such cases, a variable bound by an anterior variable-binding operator occurs within a non-extensional context such as that created by a'that'clause, or, alternatively, by propositional attitude or modal operators.
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In general, an object corresponds to a possible world, a concept corresponds to a modal proposition, and a role-bounded quantifier to a modal operator with that role as its accessibility relation.
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