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The possibility operator M ("It is possible that") may be defined in terms of L as Mp = ¬L¬p (where ¬ means "not").
But unlike the pronoun 'it' in (a), the pronoun 'it' in (b) occurs separated from the quantifier by the intervening second possibility operator, 'the following is possible'.
where A is the actuality operator which may be read 'In some actual situation', and ◊ is the possibility operator to be read 'In some possible situation'.
But, it is argued, embedded within the scope of a possibility operator the designation varies to be about possible beings and times.
Note that interpreting modal operators as quantifiers over possible worlds provides a nice theoretical justification for the usual definition of the possibility operator in terms of necessity, specifically: That is, a sentence is possible just in case its negation isn't necessary.
where ◊ denotes the alethic "possibility" operator.
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Historically, providing "world" models for modal logic was also useful for bringing out dimensions of variation among modal logics: by putting various constraints on the accessibility relation, the behaviour of the necessity and possibility operators could be varied in ways it was hard to imagine before possessing the device of models.
There is also a possibility of operator bias as in women with evidence of severe disease documentation of the presence of small lesions such as those located at utero-sacral ligaments becomes less clinically relevant.
The accident at Japan's Fukushima Daiichi plant in 2011 alerted the American nuclear industry and its regulators to the possibility that operators at plants with more than one reactor might have to deal with more than one meltdown at a time in a flood, earthquake or other catastrophe.
With the goal to reduce the possibilities of operator error, improvements in both plant design and organization in process industry can be made (Löwe et al., 2005).
Five independent clinicians referred to as A, B, C, D, E have been randomly selected to trace both radiographs maintaining the same working and lighting conditions to minimize the possibility of operator- and environment-dependent errors from occurring.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com