The syntax of autoepistemic logic extends that of propositional logic by a modal operator \ Box indicating knowledge : if F is a formula, \ Box F indicates that F is known.
22.
Within the system of formal ethics, an imperative is taken to represent a preference rather than a demand ( called " anti-modal " view, because an underline doesn't behave like a modal operator ).
23.
In " de dicto " claims, any existential quantifiers are within the scope of the modal operator, whereas in " de re " claims the modal operator falls within the scope of the existential quantifier.
24.
Given these operators and negation, one can always add \ Diamond _ i modal operators defined as \ Diamond _ i P if and only if \ lnot \ Box _ i \ lnot P.
25.
In " de dicto " claims, any existential quantifiers are within the scope of the modal operator, whereas in " de re " claims the modal operator falls within the scope of the existential quantifier.
26.
A . N . Prior created modern temporal logic, closely related to modal logic, in 1957 by adding modal operators [ F ] and [ P ] meaning " eventually " and " previously ".
27.
According to the traditional'possible worlds'semantics of modal logic, the compound sentences that are formed out of the modal operators are to be interpreted in terms of quantification over possible worlds, subject to the relation of accessibility.
28.
If CT is the correct account of modal properties we still can keep the intuition that identity statements are contingent and a priori because counterpart theory understands the modal operator in a different way than standard modal logic.
29.
In its application to the alethic modalities of possibility and necessity, Aristotle observed this case, and in the case of normal modal logic, the relationship of these modal operators to the quantification can be understood by setting up models using Kripke semantics.
30.
Modal logic is characterized by the modal operators \ Box p ( box p ) asserting that p \, \ ! is necessarily the case, and \ Diamond p ( diamond p ) asserting that p \, \ ! is possibly the case.
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