following implication

USAGE SUMMARY

The phrase "following implication" is correct and usable in written English.
It can be used when you want to refer to a conclusion or consequence that comes after a statement or argument. Example: "The following implication of this theory is that we must reconsider our approach to the problem."

✓ Grammatically correct

Science

Human-verified examples from authoritative sources

Exact Expressions

60 human-written examples

The following implication holds: (3.23).

Journal of Inequalities and Applications

For the following implication holds: (1.6).

Fixed Point Theory and Applications

(i) For the following implication holds:  .

Fixed Point Theory and Applications

Thus, we must conclude that the following implication holds (4.7).

Journal of Inequalities and Applications

The following implication holds: the (WBCQ) ⟹ the quasi (WBCQ).

Fixed Point Theory and Applications

It is known [30] that, for the Lukasiewicz -norm, the following implication holds: (1.8).

Journal of Inequalities and Applications

It is easy to see that we have the following implication: -strongly monotonicity relaxed -cocoercivity.

Journal of Inequalities and Applications

It is known ([43]) that for the ukasiewicz -norm the following implication holds: (2.2).

Journal of Inequalities and Applications

A mapping is called a fuzzy order -contractive mapping if the following implication holds: (2.1).

Fixed Point Theory and Applications

We say that a Banach space is strictly convex if the following implication holds for : (2.1).

Fixed Point Theory and Applications

then the following implication holds: if Open image in new window then Open image in new window (61).

Probability, Uncertainty and Quantitative Risk

Expert writing Tips

Best practice

When using "following implication", ensure that the relationship between the initial statement and the consequence is clear and logically sound to enhance the clarity of your argument.

Common error

Avoid assuming that because one event follows another, the first event necessarily caused the second. Always establish a clear causal link when using the phrase "following implication" to avoid logical fallacies.

Linguistic Context

The phrase "following implication" functions as a transitional phrase used to introduce a logical consequence or deduction derived from a preceding statement. It is commonly found in academic and scientific writing to clearly outline the relationship between premises and conclusions, as evidenced by Ludwig.

Expression frequency: Very common

Frequent in

Science

100%

Less common in

News & Media

0%

Formal & Business

0%

Encyclopedias

0%

Ludwig's WRAP-UP

The phrase "following implication" is a valuable tool for clearly outlining logical consequences in writing. Ludwig's analysis confirms its frequent use in formal, especially scientific and academic contexts. When employing this phrase, ensure that the logical connection between the antecedent statement and its implication is evident. Avoid mistaking correlation for causation, and consider alternatives such as "logical entailment" or "ensuing consequence" for stylistic variation. Overall, using "following implication" effectively enhances the clarity and rigor of your arguments.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

logical entailment

Emphasizes the necessary connection between premises and conclusion.

necessary result

Highlights that the outcome is unavoidable given the preceding conditions.

ensuing consequence

Focuses on the result that predictably follows an action or condition.

ensuing result

Similar to "ensuing consequence" but more general, referring to any outcome that follows.

derived inference

Focuses on the process of drawing a conclusion based on evidence and reasoning.

resulting conclusion

Emphasizes the final judgment or decision that arises logically from a set of premises.

implicit consequence

Suggests that the consequence is understood or implied, though not expressly stated.

subsequent deduction

Highlights the act of reasoning to a specific conclusion after considering general principles or evidence.

predictable outcome

Emphasizes the expected or foreseeable nature of the consequence.

attendant outcome

Suggests that the result is naturally associated or accompanies the initial situation.

FAQs

How can I use "following implication" in a sentence?

You can use "following implication" to introduce a logical consequence or result that stems from a previous statement. For example: "Given these conditions, the "following implication" is a reduction in energy consumption".

What are some alternatives to "following implication"?

Some alternatives include "logical entailment", "ensuing consequence", or "resulting conclusion", depending on the specific nuance you want to convey.

Is it always necessary to explicitly state the "following implication"?

While not always mandatory, explicitly stating the "following implication" can improve clarity, especially in complex arguments or technical writing. However, in some contexts, the implication may be obvious and need not be stated.

How does "following implication" differ from "subsequent result"?

"Following implication" suggests a logical deduction or necessary consequence, while "subsequent result" simply indicates an outcome that occurs afterward, without necessarily implying a direct causal or logical link.