Up tack in the context of Wheel theory

⭐ Core Definition: Up tack

"Up tack" is the Unicode name for a symbol (⊥, \bot in LaTeX, U+22A5 in Unicode) that is also called "bottom", "falsum", "absurdum", or "absurdity", 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,⊥)

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⭐ Core Definition: Up tack
Up tack in the context of False (logic)
Up tack in the context of Bottom type

Up tack in the context of False (logic)

In logic, false (Its noun form is falsity) or untrue is the state of possessing negative truth value and is a nullary logical connective. In a truth-functional system of propositional logic, it is one of two postulated truth values, along with its negation, truth. Usual notations of the false are 0 (especially in Boolean logic and computer science), O (in prefix notation, Opq), and the up tack symbol $\bot$ .

Another approach is used for several formal theories (e.g., intuitionistic propositional calculus), where a propositional constant (i.e. a nullary connective), $\bot$ , is introduced, the truth value of which being always false in the sense above. It can be treated as an absurd proposition, and is often called absurdity.

View the full Wikipedia page for False (logic)

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Up tack in the context of Bottom type

In type theory, a theory within mathematical logic, the bottom type of a type system is the type that is a subtype of all other types.

Where such a type exists, it is often represented with the up tack (⊥) symbol.

View the full Wikipedia page for Bottom type

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⭐ Core Definition: Up tack

Up tack in the context of False (logic)

Up tack in the context of Bottom type