every formula of

USAGE SUMMARY

The phrase "every formula of" is correct and usable in written English.
It can be used when referring to all formulas within a specific context, such as mathematics, science, or logic. Example: "Every formula of physics must adhere to the laws of nature to be valid."

✓ Grammatically correct

Science

News & Media

Encyclopedias

Human-verified examples from authoritative sources

Exact Expressions

9 human-written examples

Given that specification, the semantics then defines truth conditions for every formula of the language.

SEP

We have now said how to associate a truth value, or undefined, with every formula of LPCR (under our simplifying assumptions).

SEP

A logic is said to be complete with respect to a semantics for L* if and only if every formula of L* that is valid relative to that semantics is a theorem of the logic.

SEP

A finite characteristic matrix yields a decision procedure, where a system is decidable if every formula of the system that is not a theorem is falsified by some finite matrix (this is the finite model property).

SEP

A special case arises with V = ∅, for which ∏ V is the unique valuation vT assigning T to every formula (of the language in question, to which the claim of uniqueness is understood as relativized).

SEP

By Brouwer's first published logical theorem ¬ ¬ ¬A → ¬A, every formula of the form ¬A is stable; but in IPC and IQC prime formulas and their negations are undecidable, as shown in Section 5.1 below.

SEP

Human-verified similar examples from authoritative sources

Similar Expressions

50 human-written examples

Gödel's translation associates with every formula F x) of the language of Peano arithmetic a formula F′(x) = ∃y∀zA y, z, x) of the language of the theory T, where A is quantifier free and the (boldface) bound variables are finite sequences of variables thought to range over functionals of a finite type determined by the type of the variable.

SEP

The game-theoretical semantics of IFL is captured by this compositional semantics: for every formula φ of IFL, player 2 has a winning strategy in G φ, M, g) iff the condition M ⊨{g} φ holds.

SEP

This principle asserts the existence of a concept corresponding to every open formula of the form φ(x) with free variable x, no matter how complex φ is.

SEP

Suppose L is a first-order language, T is a theory in L, and Φ is a set of formulas of L. We say that T has elimination of quantifiers down to Φ if for every formula φ x1,…,xn) of L there is a formula ψ x1,…,xn) in Φ such that in every model of T, φ and ψ are satisfied by exactly the same n-tuples of elements (a1,…,an).

SEP

In first-order logic, every formula is well composed of atomic formulas by negation, conjunction, disjunction, and introducing quantifiers.

Journal of Symbolic Computation

Expert writing Tips

Best practice

When using "every formula of", ensure that the context clearly defines the scope or set of formulas being referenced. For instance, specify "every formula of propositional logic" or "every formula of organic chemistry".

Common error

Avoid using "every formula of" without specifying the relevant domain or context. Saying "every formula is important" is too broad; instead, clarify, "every formula of quantum mechanics is crucial for understanding the behavior of subatomic particles".

Linguistic Context

The phrase "every formula of" functions as a determiner phrase specifying that a statement applies universally to each formula within a defined set. Ludwig AI supports that this phrase is grammatically correct. It is used to establish scope and generality.

Expression frequency: Uncommon

Frequent in

Science

60%

Encyclopedias

20%

News & Media

20%

Less common in

Formal & Business

0%

Wiki

0%

Reference

0%

Ludwig's WRAP-UP

In summary, "every formula of" is a grammatically sound phrase used to indicate a universal application across all formulas within a specified context. Ludwig AI confirms its validity. Primarily found in scientific and encyclopedic sources, it asserts a property or condition that must hold true for each formula within a system. While uncommon, its precise meaning and usefulness in technical discussions make it valuable. Alternatives such as "each formula within" or "all formulas in" may be used depending on the desired emphasis. When employing this phrase, clarity regarding the specific domain of formulas is crucial to avoid overgeneralization.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

each formula within

Replaces "every" with "each" and "of" with "within", focusing on individual formulas inside a broader scope.

all formulas in

Substitutes "every" with "all" and "of" with "in", generalizing to a complete set of formulas.

each equation from

Replaces "formula" with "equation" and "of" with "from", suitable when referring to mathematical equations.

all expressions within

Uses "expressions" instead of "formulas", implying a broader mathematical or logical concept, also uses "within" instead of "of".

every instance of a formula in

Adds emphasis on specific instances, clarifying that each individual formula is being considered, also uses "in" instead of "of".

each version of the formula

Focuses on different versions or variations of a particular formula, implying slight modifications or adaptations.

every formulation for

Replaces "formula" with "formulation", highlighting the process of creating or expressing the formula, also uses "for" instead of "of".

every type of equation in

Specifies a focus on different types or categories of equations, rather than individual instances, also uses "in" instead of "of".

each mathematical relation within

Uses "mathematical relation" instead of "formula", useful in a strictly mathematical context.

the entirety of formulas present in

This alternative is much more formal and verbose than the query, suitable for highly technical documentation.

FAQs

How can I use "every formula of" in a sentence?

You can use "every formula of" to specify a rule, condition, or characteristic that applies to all formulas within a particular domain or system. For instance, "Every formula of propositional logic must be either true or false".

What phrases are similar to "every formula of"?

Alternatives include phrases like "each formula within", "all formulas in", or "every equation from" depending on the context.

Is "every formula of" grammatically correct?

Yes, "every formula of" is grammatically correct and commonly used in technical and scientific writing to refer to all formulas within a specified context.

What is the difference between "every formula of" and "all formulas in"?

While both phrases are similar, "every formula of" tends to emphasize individual formulas within a broader system, whereas "all formulas in" focuses on the complete set. The choice often depends on the specific nuance you wish to convey.