Sentence examples for understood as valid from inspiring English sources

Throughout this section, unless otherwise stated, every limit relation is understood as valid uniformly for all (xgeqgamma n) as (nrightarrowinfty).

In other words, arithmetic is incomplete, i.e. some propositions of arithmetic can be understood as valid; yet they cannot be proven within the frame of arithmetic.

Most plausibly, perhaps, Aristotle's complete and incomplete syllogisms taken together are understood as formally valid premise-conclusion arguments; and his complete and completed syllogisms taken together as (sound) deductions.

Malinowski's relation of q-entailment qualifies derivations of true sentences from non-refuted premises (understood as hypotheses) as valid, and p-entailment (p for "plausibility") has been studied by Frankowski, who tried to explicate "reasonings wherein the degree of strength of the conclusion (i.e. the conviction it is true) is smaller th[a]n that of the premisses" (Frankowski 2004, 41).

Furthermore, proofs are here understood as candidates of valid proofs, which means that the rules from which they are composed are not fixed.

The triple helix should not be understood as a generally valid theoretical structure, but rather as a systemic approach " which creates a common analytical framework for the mostly isolated case studies in this area" (Ortiz 2013: 50, translated).

Although a 3D digital model does not provide a complete picture of the object, it should be understood as a powerful tool potentially, with valid data for visualisation and cultural heritage research, and complementary to other measurement methods [29].

One of the authors (KA) studied "The Healer's Art" [ 22] which was sufficiently well understood as to be considered a valid intervention in the USA.

If the requirement of a connection between antecedent and succedent of a valid implication is understood as a content connection, and if a content connection obtains if antecedent and succedent are relevant to each other, then "the general classes of connexive and relevant logics are one and the same" (Routley 1978, p. 393), cf. also Serenac and Jennings 2003.

The difference-in-difference estimator needs to be understood as one of several estimators that are valid under alternative assumptions (Smith and Todd 2005; Jung and Pirog 2011).

In any event, disproving must be understood as 'establishing inconsistent,' not as 'establishing not provable' (or 'establishing not valid').