material implication

logical connective between two assertions, frequently symbolized by a (most often double) arrow to the right
Thing logical_operator Q7881229
material implication
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material implication

Summary

material implication is a logical operator[1]. It draws 3,950 Wikipedia views per month (logical_operator category, ranking #2 of 7).[2]

Key Facts

  • material implication's instance of is recorded as logical operator[3].
  • material implication's instance of is recorded as Boolean function[4].
  • material implication is a type of proposition[5].
  • material implication is part of if and only if[6].
  • material implication's Commons category is recorded as Material conditional[7].
  • material implication is the opposite of converse implication[8].
  • material implication's Unicode character is recorded as ⟹[9].
  • material implication's Unicode character is recorded as →[10].
  • material implication's Unicode character is recorded as ⇒[11].
  • material implication's Unicode character is recorded as ⟶[12].
  • material implication's described by source is recorded as ISO 80000-2:2019 Quantities and units — Part 2: Mathematics[13].
  • material implication's described by source is recorded as Q140169500[14].
  • material implication's described by source is recorded as mathisfun.com dictionary[15].
  • material implication's main Wikidata property is recorded as P7719[16].
  • material implication's different from is recorded as logical consequence[17].
  • material implication's TeX string is recorded as \rightarrow[18].
  • material implication's TeX string is recorded as \DoubleRightArrow[19].
  • material implication's TeX string is recorded as \DoubleLongRightArrow[20].
  • material implication's TeX string is recorded as \longrightarrow[21].
  • material implication's studied by is recorded as Boolean algebra[22].
  • material implication's maintained by WikiProject is recorded as WikiProject Mathematics[23].

Body

Definition and Type

Recorded instance of include logical operator[3] and Boolean function[4]. material implication is a type of proposition[5]. It is the opposite of converse implication[8].

Use and Application

material implication is part of if and only if[6].

Why It Matters

material implication draws 3,950 Wikipedia views per month (logical_operator category, ranking #2 of 7).[2] It has Wikipedia articles in 23 language editions, a strong signal of global cultural recognition.[24] It is known by 65 alternative names across languages and contexts.[25]

References

Programmatic citations — every numbered marker resolves to a verifiable graph row below.

Direct Wikidata claims

  1. [3] ↑ . wikidata.org.
  2. [4] ↑ . wikidata.org.
  3. [5] ↑ . wikidata.org.
  4. [6] ↑ . wikidata.org.
  5. [7] ↑ . wikidata.org.
  6. [8] ↑ . wikidata.org.
  7. [9] ↑ . wikidata.org.
  8. [10] ↑ . wikidata.org.
  9. [11] ↑ . wikidata.org.
  10. [12] ↑ . wikidata.org.
  11. [13] ↑ . wikidata.org.
  12. [14] ↑ . wikidata.org.
  13. [15] ↑ . wikidata.org.
  14. [16] ↑ . wikidata.org.
  15. [17] ↑ . wikidata.org.
  16. [18] ↑ . wikidata.org.
  17. [19] ↑ . wikidata.org.
  18. [20] ↑ . wikidata.org.
  19. [21] ↑ . wikidata.org.
  20. [22] ↑ . wikidata.org.
  21. [23] ↑ . wikidata.org.

Class ancestry

  1. [1] ↑ . Wikidata. wikidata.org.

Aggregate / graph-position facts

  1. [2] ↑ . Wikimedia Foundation. dumps.wikimedia.org.
  2. [24] ↑ . Wikidata sitelinks. wikidata.org.
  3. [25] ↑ . Wikidata aliases. wikidata.org.

📑 Cite this page

Use these citations when quoting this entity in research, articles, AI prompts, or wherever provenance matters. We aggregate Wikidata + Wikipedia + authoritative open-data sources; the stitched, scored, cross-referenced view is what 4ort.xyz contributes.

APA 4ort.xyz Knowledge Graph. (2026). material implication. Retrieved October 1, 2026, from https://4ort.xyz/entity/material-implication
MLA “material implication.” 4ort.xyz Knowledge Graph, 4ort.xyz, 1 Oct. 2026, https://4ort.xyz/entity/material-implication.
BibTeX @misc{4ortxyz_material-implication_2026, author = {{4ort.xyz Knowledge Graph}}, title = {{material implication}}, year = {2026}, url = {https://4ort.xyz/entity/material-implication}, note = {Accessed: 2026-10-01}}
LLM prompt According to 4ort.xyz Knowledge Graph (aggregator of Wikidata, Wikipedia, and authoritative open-data sources): material implication — https://4ort.xyz/entity/material-implication (retrieved 2026-10-01)

Canonical URL: https://4ort.xyz/entity/material-implication · Last refreshed:

Edit History

Rolling log of changes to this entity's Wikidata record. Values shown reflect the current state of each edited property — follow the history link to see the precise diff for any edit.

  1. 16d ago · AddyLockPool · 2026-09-17 view diff on Wikidata ↗
    Described by source → ISO 80000-2:2019 Quantities and units — Part 2: Mathematics, Q140169500, mathisfun.com dictionary
    "/* wbsetclaim-create:2||1 */ [[Property:P1343]]: [[Q54640709]]"
  2. 16d ago · AddyLockPool · 2026-09-17 view diff on Wikidata ↗
    Inverse label item → —
    Part of → if and only if
    Described by source → ISO 80000-2:2019 Quantities and units — Part 2: Mathematics, Q140169500, mathisfun.com dictionary
    Opposite of → converse implication
    "/* wbsetclaim-create:2||1 */ [[Property:P1343]]: [[Q140169500]]"
  3. 15w ago · AddyLockPool · 2026-06-16 view diff on Wikidata ↗
    Inverse label item → —
    "/* wbsetclaim-create:2||1 */ [[Property:P7087]]: [[Q5166460]]"
  4. 17w ago · Alex rosenberg35 · 2026-06-04 view diff on Wikidata ↗
    Maintained by wikiproject → WikiProject Mathematics
    Local thumb → —
    Described by source → ISO 80000-2:2019 Quantities and units — Part 2: Mathematics, Q140169500, mathisfun.com dictionary
    Subclass of → —
    + 7 other properties edited (see Wikidata diff for full list)
    "/* wbremoveclaims-remove:1| */ [[Property:P1889]]: [[Q7881229]]"
Live feed via Wikidata EventStreams. New edits appear within minutes of being made on Wikidata.