closed sentence: meaning, definition, pronunciation and examples
LowSpecialized, Technical (Logic, Philosophy, Mathematics)
Quick answer
What does “closed sentence” mean?
A statement that has a definite truth value (true or false) within a formal logical system.
Audio
Pronunciation
Definition
Meaning and Definition
A statement that has a definite truth value (true or false) within a formal logical system.
In propositional logic and predicate logic, a sentence with no free variables, meaning its truth value can be determined without additional information about variable assignments.
Dialectal Variation
British vs American Usage
Differences
No significant differences in meaning. Usage is uniform in academic logic globally.
Connotations
Purely technical.
Frequency
Extremely rare outside formal logic contexts.
Grammar
How to Use “closed sentence” in a Sentence
[The formula φ] is a closed sentence.A closed sentence in [a language L] has no free variables.Vocabulary
Collocations
Examples
Examples of “closed sentence” in a Sentence
verb
British English
- The logic system must be able to determine if a formula is a closed sentence.
- The algorithm closes an open sentence by binding its variables.
American English
- The logic system must determine whether a formula is a closed sentence.
- The algorithm closes an open sentence by binding its variables.
adverb
British English
- No adverbial usage.
American English
- No adverbial usage.
adjective
British English
- The lecturer presented a closed-sentence example.
- We need a closed-sentence interpretation for this model.
American English
- The professor gave a closed-sentence example.
- We need a closed-sentence interpretation for this model.
Usage
Meaning in Context
Business
Not used.
Academic
Used in philosophy (logic), mathematics (especially logic, set theory), linguistics (formal semantics), and computer science (theoretical CS).
Everyday
Not used.
Technical
Core term in symbolic logic and formal semantics.
Vocabulary
Synonyms of “closed sentence”
Strong
Neutral
Weak
Vocabulary
Antonyms of “closed sentence”
Watch out
Common Mistakes When Using “closed sentence”
- Confusing it with a grammatically complete sentence (e.g., not a fragment).
- Using it to mean a statement that is not open for debate in a casual sense.
FAQ
Frequently Asked Questions
No. In linguistics, a grammatically complete sentence has a subject and predicate. In logic, a 'closed sentence' is a formula with no unbound (free) variables, making it truth-evaluable.
An 'open sentence' or 'open formula', which contains at least one free variable (e.g., 'x is tall') and thus does not have a definite truth value on its own.
Primarily in university-level courses on logic, philosophy of language, mathematical logic, formal semantics in linguistics, and the foundations of computer science.
Yes, when formalized in predicate logic (e.g., ∀x (Cat(x) → Mammal(x))), it is a closed sentence because the universal quantifier '∀x' binds the variable x.
A statement that has a definite truth value (true or false) within a formal logical system.
Closed sentence is usually specialized, technical (logic, philosophy, mathematics) in register.
Closed sentence: in British English it is pronounced /kləʊzd ˈsɛntəns/, and in American English it is pronounced /kloʊzd ˈsɛntəns/. Tap the audio buttons above to hear it.
Phrases
Idioms & Phrases
- “No idioms for this technical term.”
Learning
Memory Aids
Mnemonic
A CLOSEd sentence has its variables 'closed off' by quantifiers (like ∀ or ∃), locking in its truth value.
Conceptual Metaphor
Completeness/Closure (like a closed container, nothing is left open or unspecified).
Practice
Quiz
Which of the following best defines a 'closed sentence'?