Sentence examples for valuations consistent with from inspiring English sources

Now, there are additional valuations consistent with this consequence relation on which the negation truth-function is not associated with the negation connective.

This implies the statement given for consequence relations (putting "⊩" in place of "⊢") since a generalized consequence relation, like a consequence relation, is always determined by the class of all valuations consistent with it.

Here we calling v consistent with ⊢ when for no Γ, ψ, for which Γ ⊢ ψ, do we have v = T for all φ ∈ Γ while v = F; the "but further" in the preceding sentence is explained by the fact that every consequence relation ⊢ is determined by the class Val of all valuations consistent with ⊢, which in the case of ⊢∧ are precisely the ∧-boolean valuations.

In a moment of inattention I had confusingly passed from the correct thought that the only valuations consistent with ⊢∧ are the ∧-boolean ones to the faulty conclusion that the only class of valuations determining ⊢∧ is the class of all ∧-boolean valuations.

And then one can show, not only that this is the consequence relation determined by the class of ∧-boolean valuations so that if one began with that class and sought a syntactic codification of the logic it gave rise to, one's search would be at an end but further that the valuations consistent with ⊢∧ are precisely the ∧-boolean valuations.

Then the truth-functions f for which every valuation consistent with ⊢ (as above) associates #f with f are precisely the projection-conjunction truth-functions.

Thus any valuation consistent with this consequence relation must respect each of two opposite determinants making Tonk overdetermined—⟨T, F, T⟩, taking x = F and ⟨T, F, F⟩ taking y = T.

JPMorgan's controller, for example, issued an internal report in May 2012 that essentially cleared the traders of wrongdoing, saying their valuations were "consistent with industry practices".

Despite that red flag, according to a United States Senate report, the controller concluded that the valuations were "consistent with industry practices".

Their stock market valuations are consistent with those of institutions not a mile away from insolvency and default.If I had to guess what markets have learned from the Lehman episode and the six months since, I would say that it was this policymakers will not dare take any steps that look remotely like something which could trigger another credit spasm.

These pairs of dominant/dominated health states allowed us to test whether respondents' TTO valuations were consistent with the logical ordering of the relevant health states.