quantifier rankの例文

例文

1. Thus two logically equivalent formulae can have different quantifier ranks, when they express the same thing in different ways.
2. Notice that the quantifier rank is a property of the formula itself ( i . e . the expression in a language ).
3. In particular the " logical depth " of a graph is defined to be the minimum level of nesting of quantifiers ( the quantifier rank ) in a sentence defining the graph.
4. One common way to define FO [ m ] is by means of the quantifier rank qr ( & alpha; ) of a FO formula & alpha;, which expresses the depth of quantifier nesting.
5. Then FO [ m ] can be defined as all FO formulas & alpha; with qr ( & alpha; ) d " m ( or, if a partition is desired, as those FO formulas with quantifier rank equal to m ).