stratified language
Definition
Noun: A stratified language is a formal language in logic and computer science that is constructed with distinct, hierarchical levels. In such a language, statements or expressions at one level cannot refer to or make claims about the language's own rules, definitions, or statements at the same level. This prevents certain types of logical paradoxes, like those involving self-reference.
Usage
The term is used primarily in technical contexts such as mathematical logic, the philosophy of language, and the theory of programming languages. It describes a design principle for creating consistent formal systems.
Examples
- In formal logic, a stratified language might have separate object-level statements and meta-level rules about those statements.
- The theory of types in logic employs a stratified language to avoid Russell's paradox by prohibiting a set from containing itself.
- Some programming language semantics are defined using a stratified language to separate the core language from its operational rules.
Advanced Usage
- Stratification: The process of organizing a language into distinct levels is called . A key property is that truth predicates or semantic concepts (like "is true") for a given level are only defined at a higher level.
- Contrast with "Universal Language": A stratified language is often contrasted with a or , which can serve as its own metalanguage (e.g., natural languages, which allow statements about their own grammar).
Variants and Related Words
- Stratify (verb): To arrange or form into layers or levels.
- Stratification (noun): The state of being arranged in strata or the process of stratifying.
- Metalanguage (noun): A language used to describe or analyze another language. A stratified language cannot be its own metalanguage.
- Object Language (noun): The language being described or analyzed by a metalanguage.
Synonyms
- Hierarchical language
- Type-theoretic language (in specific contexts)
- Leveled language
Antonyms
- Universal language
- Unstratified language
- Natural language (in its capacity for self-reference)
Noun
-
a language that cannot be used as its own metalanguage
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