Up tack

From HandWiki
Short description: Symbol used in mathematics and logic

"Up tack" is the Unicode name for a symbol (⊥, \bot in LaTeX, U+22A5 in Unicode[1]) that is also called "bottom",[2][3] "falsum",[4] "absurdum",[5] or "absurdity",[6][7][3] depending on context. It is used to represent:

  • The truth value 'false', or a logical constant denoting a proposition in logic that is always false. (The names "falsum", "absurdum" and "absurdity" come from this context.)
  • The bottom element in wheel theory and lattice theory, which also represents absurdum when used for logical semantics
  • The bottom type in type theory, which is the bottom element in the subtype relation. This may coincide with the empty type, which represents absurdum under the Curry–Howard correspondence
  • The "undefined value" in quantum physics interpretations that reject counterfactual definiteness, as in (r0,⊥)

as well as

The glyph of the up tack appears as an upside-down tee symbol, and as such is sometimes called eet (the word "tee" in reverse).[8][9] Tee plays a complementary or dual role in many of these theories.

The similar-looking perpendicular symbol (⟂, \perp in LaTeX, U+27C2 in Unicode) is a binary relation symbol used to represent:

Historically, in character sets before Unicode 4.1 (March 2005), such as Unicode 4.0[10] and JIS X 0213, the perpendicular symbol was encoded with the same code point as the up tack, specifically U+22A5 in Unicode 4.0.[11] This overlap is reflected in the fact that both HTML entities ⊥ and ⊥ refer to the same code point U+22A5, as shown in the HTML entity list. In March 2005, Unicode 4.1 introduced the distinct symbol "⟂" (U+27C2 "PERPENDICULAR") with a reference back to ⊥ (U+22A5 "UP TACK") and a note that "typeset with additional spacing."[12]

The double tack up symbol (⫫, U+2AEB in Unicode[1]) is a binary relation symbol used to represent:

See also

Notes

  1. ↑ 1.0 1.1 "Mathematical Operators – Unicode". https://www.unicode.org/charts/PDF/U2200.pdf. 
  2. ↑ Giunchiglia, Enrico; Tacchella, Armando (2004-02-24) (in en). Theory and Applications of Satisfiability Testing: 6th International Conference, SAT 2003. Santa Margherita Ligure, Italy, May 5-8, 2003, Selected Revised Papers. Springer. pp. 507. ISBN 978-3-540-24605-3. https://www.google.com.br/books/edition/Theory_and_Applications_of_Satisfiabilit/PSgGCAAAQBAJ. 
  3. ↑ 3.0 3.1 Goble, Lou (2007) (in en). The Blackwell Guide to Philosophical Logic. Blackwell. pp. 10. https://www.google.com.br/books/edition/The_Blackwell_Guide_to_Philosophical_Log/bSsL0QEACAAJ?hl=en. 
  4. ↑ Ribeiro, Henrique Jales (2012-04-25) (in en). Inside Arguments: Logic and the Study of Argumentation. Cambridge Scholars Publishing. pp. 382. ISBN 978-1-4438-3931-0. https://www.google.com.br/books/edition/Inside_Arguments/QU4sBwAAQBAJ. 
  5. ↑ Gallier, Jean (2011-02-01) (in en). Discrete Mathematics. Springer Science & Business Media. pp. 4. ISBN 978-1-4419-8047-2. https://www.google.com.br/books/edition/Discrete_Mathematics/HXSjIP0OgCUC. 
  6. ↑ Makridis, Odysseus (2022). "Symbolic Logic" (in en). Palgrave Philosophy Today: 207. doi:10.1007/978-3-030-67396-3. ISSN 2947-9339. https://link.springer.com/book/10.1007/978-3-030-67396-3. 
  7. ↑ Tennant, Neil (2015-02-11) (in en). Introducing Philosophy: God, Mind, World, and Logic. Routledge. pp. 179. ISBN 978-1-317-56087-6. https://www.google.com.br/books/edition/Introducing_Philosophy/VbagBgAAQBAJ. 
  8. ↑ Church, Alonzo; Langford, Cooper Harold (1957) (in en). The Journal of Symbolic Logic. Association for Symbolic Logic.. pp. 41. https://www.google.com.br/books/edition/The_Journal_of_Symbolic_Logic/gpE0AAAAIAAJ?. 
  9. ↑ Smullyan, Raymond M. (1987). Forever undecided: a puzzle guide to Gödel (1 ed.). New York, N.Y: Knopf. pp. 57. ISBN 978-0-394-54943-9. 
  10. ↑ "The Unicode Standard, Version 4.0 (Archived Code Charts)". https://www.unicode.org/versions/Unicode4.0.0/CodeCharts.pdf. 
  11. ↑ Unicode 4.0 did defined "UP TACK = orthogonal to = perpendicular = base, bottom."
  12. ↑ "Miscellaneous Mathematical Symbols-A, Range: 27C0–27EF – The Unicode Standard, Version 4.1". https://www.unicode.org/charts/PDF/Unicode-4.1/U41-27C0.pdf. 
  13. ↑ "Conditional independence notation". 27 March 2020. https://www.johndcook.com/blog/2020/03/27/conditional-independence-notation/. 



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