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This approach depends upon the use of a sorted theory, one in which each constant is assigned a sort, that is an indicator of a class to which it belongs; thus, promed4 may be declared to be of sort organism (or sort bacterium, a subsort of organism).
But a sorted theory is of special value in that it allows query elicitation.
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Kaye [1991] generalised Specker's method to show how any typed theory of sets, garnished with the axioms of typical ambiguity, turns out to be equiconsistent with a one-sorted theory.
(Actually, von Neumann develops a theory of functions, taken as primitive, rather than classes, wherein corresponding to the member/non-member distinction one has a distinction between an object that can be an argument of some function and one that cannot. In its modern form, due to Bernays and Gödel, it is a single-sorted theory of classes).
In particular, second-order logic and the theory of plural quantification will be each closely related to two first-order two-sorted theories, which lack the expressive resources often attributed to each extension of classical quantificational logic.
Figure 4 Examples of a sorted sense score distribution.
The allocation procedure uses a sorted queue of cells waiting to undergone change.
Fig. 7 2D illustration of the superior space-filling properties of a sorted Sobol sequence, compared to a sorted IID uniform sequence.
Output : a sorted Pareto list.
In Eq. (32), two sorted lists are merged into a sorted list.
The sorted list of probes was translated into a sorted list of Ensembl transcript identifiers as described above.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com