monotonic

USAGE SUMMARY

The word "monotonic" is correct and usable in written English.
It is an adjective meaning "characterized by a single, unchanging tone". For example, you could use it in a sentence like this: "The professor's monotonic voice caused several of the students to nod off during his lecture."

✓ Grammatically correct

Science

Encyclopedias

Human-verified examples from authoritative sources

Exact Expressions

31 human-written examples

Given a perfect model, refining the quality of the data should lead to monotonic convergence of the model behavior to the target system's behavior, but even this expectation is not always justifiable for perfect models (cf. Judd and Smith 2001; Smith 2003).

SEP

A bounded, monotonic function on an algebra of events is called a capacity.

SEP

3. Avron does not, however, assume that these relations are monotonic, i.e., that $\Delta \vdash \Gamma$ implies $\Delta \cup \Delta ' \vdash \Gamma \cup \Gamma '$, with the restriction that $\Gamma \cup \Gamma '$ contains at most one formula in the case of single-conclusion consequence relations.

SEP

The important feature of the logarithm is that it is a monotonic function: the larger Mj, the larger its logarithm.

SEP

Of course, the consequence relation of the classical conditional logics is monotonic, and conditional semantics uses possible worlds, not models.

SEP

Standard logic, including Horn logic, is monotonic which means that enlarging an axiom set by adding new axioms simply enlarges the set of theorems derivable from it; negation-by-failure, however, is non-monotonic and the addition of new program clauses to an existing Prolog program may cause some goals to cease from being theorems.

SEP

Human-verified similar examples from authoritative sources

Similar Expressions

29 human-written examples

The external dynamics is thus the non-monotonic character of some consequence relations: Γ ⊢ A and Γ ∪ Δ ⊬ A for some Γ, Δ and A. However, even if the premise-set remains constant, some previously inferred conclusion may considered as not derivable at a later stage.

SEP

Since revision sequences are typically non-monotonic, the extension is not straightforward.

SEP

It suggests that defeasible (non-monotonic) logic, probability theory, and other non-classical formal frameworks may be suited to this task.

SEP

Still other approaches develop non-monotonic logics (see entry), logics for making not only deductive inferences, but also defeasible, inductive inferences (Pollock 1995, 2008; Horty 2012).

SEP

Where ψ is classically entailed by φ, Right Weakening expresses that whenever φ is a non-monotonic consequence of τ then so is ψ.

SEP

Expert writing Tips

Best practice

When describing trends or functions, ensure that "monotonic" accurately reflects a consistent increase or decrease, without reversals.

Common error

Avoid using "monotonic" when the trend or function fluctuates; "monotonic" implies a single, consistent direction of change.

Linguistic Context

The adjective "monotonic" primarily functions to describe a consistent trend or function, especially in mathematics and logic. It signifies that a function either never decreases or never increases as its independent variable increases. As Ludwig AI points out, it is used in contexts where consistent behavior is key.

Expression frequency: Common

Frequent in

Science

75%

Encyclopedias

15%

Formal & Business

5%

Less common in

News & Media

2%

Wiki

2%

Reference

1%

Ludwig's WRAP-UP

In summary, the term "monotonic" functions as an adjective primarily used in scientific and academic contexts to describe consistently increasing or decreasing functions or trends. Ludwig AI confirms that its grammatical status is correct. Its primary use lies in mathematics, logic, and related fields, emphasizing a lack of fluctuation. While it can also describe something unchanging in tone or quality, this usage is less common. When using "monotonic", ensure that the subject truly exhibits a consistent direction of change to avoid misrepresentation.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

constant

Indicates a state of unchanging value or quality over time.

consistent

Refers to a reliable and unchanging pattern or behavior.

unvarying

Emphasizes the lack of change or variation in a particular attribute.

steady

Suggests a stable and predictable progression or state.

uniform

Implies a consistent and even distribution or quality throughout.

regular

Indicates a recurring pattern or consistent behavior over time.

invariable

Highlights the absolute lack of change or deviation.

fixed

Suggests a firmly established and unchanging state.

static

Refers to a state of no movement or change.

rhythmic

Describes a consistent and predictable pattern or sequence.

FAQs

How is "monotonic" used in mathematical contexts?

In mathematics, "monotonic" describes a function that either consistently increases or consistently decreases across its domain. It doesn't change direction.

What does it mean for a voting procedure to be "monotonic"?

A voting procedure is "monotonic" if a candidate's chances of winning don't decrease when they are ranked higher by more voters. In simpler terms, more support should only help a candidate, not hurt them.

What is the difference between "monotonic" and "non-monotonic"?

"Monotonic" means consistently increasing or decreasing, while ""non-monotonic"" implies that the function or trend can both increase and decrease at different points.

Can "monotonic" describe something other than mathematical functions?

Yes, although less common, "monotonic" can also describe something unchanging in tone or quality, such as a "monotonic" voice. However, its primary usage is in mathematics and logic.