Sentence examples for each formula of the from inspiring English sources
We may set out to translate each formula of the many-sorted language into a formula of the one-sorted language: we translate each identity in terms of a single identity predicate; a quantification on a variable of sort $i$, $\forall x^i \ A$, is replaced with a formula of the form $\forall x (S_i x \rightarrow A)$.
Based on this characterization, we thus propose measures for the degree of inconsistency and for the responsibility of each formula for the inconsistency of a knowledge base with constraints, respectively.
The formulation of the axiom of separation was made explicit: "for each formula φ of the first-order language with equality and membership, {x ∈ A | φ} exists".
In a first step, putative elements and atom counts of each molecular formula of the fragment ions are compared to the putative molecular formulas of its precursor ion (postulated as described above) to find the elemental composition of the precursor for which most of the fragment formulas can be annotated.
For each potential molecular formula of the intact compound, a fragmentation tree and its score are computed.
In first-order formalizations of arithmetic, this is formulated as a scheme: for each first-order arithmetical formula of the language of arithmetic with one free variable, one instance of the induction principle is included in the formalization of arithmetic.
Since major label debut Relish, she has released seven studio albums -- each straying significantly from the formula of the last.
To include the effect of ethnic distribution, we undertook a bootstrap analysis by performing a set of 10 000 Monte Carlo simulations to estimate the 95% confidence limits for the proportion of people with each stage of CKD with each formula and the proportion of people who would be classified differently with each formula on two occasions within 3 months.
These values were then adjusted for 95% confidence and inserted into the numerator of each formula to calculate the upper and lower limit of the 95% confidence interval for both indices.
Because the theoretical ratio (i = [M+1]/[M]) of single stable isotope-labeled molecules (M+1) to monoisotopic molecules (M) is unique to each formula, the false positive rate of the molecular formula search can be reduced through comparison of theoretical and measured i values.
