What does deductive closure mean?

Definitions for deductive closure
de·duc·tive clo·sure

This dictionary definitions page includes all the possible meanings, example usage and translations of the word deductive closure.

Wiktionary

  1. deductive closurenoun

    The set of all the statements that can be deduced from a given set of statements.

Wikipedia

  1. Deductive closure

    In mathematical logic, a set T {\displaystyle {\mathcal {T}}} of logical formulae is deductively closed if it contains every formula φ {\displaystyle \varphi } that can be logically deduced from T {\displaystyle {\mathcal {T}}} , formally: if T ⊢ φ {\displaystyle {\mathcal {T}}\vdash \varphi } always implies φ ∈ T {\displaystyle \varphi \in {\mathcal {T}}} . If T {\displaystyle T} is a set of formulae, the deductive closure of T {\displaystyle T} is its smallest superset that is deductively closed. The deductive closure of a theory T {\displaystyle {\mathcal {T}}} is often denoted Ded ⁡ ( T ) {\displaystyle \operatorname {Ded} ({\mathcal {T}})} or Th ⁡ ( T ) {\displaystyle \operatorname {Th} ({\mathcal {T}})} . This is a special case of the more general mathematical concept of closure — in particular, the deductive closure of T {\displaystyle {\mathcal {T}}} is exactly the closure of T {\displaystyle {\mathcal {T}}} with respect to the operation of logical consequence ( ⊢ {\displaystyle \vdash } ).

Wikidata

  1. Deductive closure

    Deductive closure is a property of a set of objects. A set of objects, O, is said to exhibit closure or to be closed under a given operation, R, provided that for every object, x, if x is a member of O and x is R-related to any object, y, then y is a member of O. In the context of statements, a deductive closure is the set of all the statements that can be deduced from a given set of statements. In propositional logic, the set of all true propositions exhibits deductive closure: if set O is the set of true propositions, and operation R is logical consequence, then provided that proposition p is a member of O and p is R-related to q, q is also a member of O.

How to pronounce deductive closure?

How to say deductive closure in sign language?

Numerology

  1. Chaldean Numerology

    The numerical value of deductive closure in Chaldean Numerology is: 4

  2. Pythagorean Numerology

    The numerical value of deductive closure in Pythagorean Numerology is: 6


Translations for deductive closure

From our Multilingual Translation Dictionary

Get even more translations for deductive closure »

Translation

Find a translation for the deductive closure definition in other languages:

Select another language:

  • - Select -
  • 简体中文 (Chinese - Simplified)
  • 繁體中文 (Chinese - Traditional)
  • Español (Spanish)
  • Esperanto (Esperanto)
  • 日本語 (Japanese)
  • Português (Portuguese)
  • Deutsch (German)
  • العربية (Arabic)
  • Français (French)
  • Русский (Russian)
  • ಕನ್ನಡ (Kannada)
  • 한국어 (Korean)
  • עברית (Hebrew)
  • Gaeilge (Irish)
  • Українська (Ukrainian)
  • اردو (Urdu)
  • Magyar (Hungarian)
  • मानक हिन्दी (Hindi)
  • Indonesia (Indonesian)
  • Italiano (Italian)
  • தமிழ் (Tamil)
  • Türkçe (Turkish)
  • తెలుగు (Telugu)
  • ภาษาไทย (Thai)
  • Tiếng Việt (Vietnamese)
  • Čeština (Czech)
  • Polski (Polish)
  • Bahasa Indonesia (Indonesian)
  • Românește (Romanian)
  • Nederlands (Dutch)
  • Ελληνικά (Greek)
  • Latinum (Latin)
  • Svenska (Swedish)
  • Dansk (Danish)
  • Suomi (Finnish)
  • فارسی (Persian)
  • ייִדיש (Yiddish)
  • հայերեն (Armenian)
  • Norsk (Norwegian)
  • English (English)

Word of the Day

Would you like us to send you a FREE new word definition delivered to your inbox daily?

Please enter your email address:


Citation

Use the citation below to add this definition to your bibliography:

Style:MLAChicagoAPA

"deductive closure." Definitions.net. STANDS4 LLC, 2024. Web. 28 Mar. 2024. <https://www.definitions.net/definition/deductive+closure>.

Discuss these deductive closure definitions with the community:

0 Comments

    Are we missing a good definition for deductive closure? Don't keep it to yourself...

    Free, no signup required:

    Add to Chrome

    Get instant definitions for any word that hits you anywhere on the web!

    Free, no signup required:

    Add to Firefox

    Get instant definitions for any word that hits you anywhere on the web!

    Browse Definitions.net

    Quiz

    Are you a words master?

    »
    remove completely from recognition or memory
    A cleave
    B abash
    C abhor
    D efface

    Nearby & related entries:

    Alternative searches for deductive closure: