

The faleshood is commonly denoted falsefalse, FF, \bot, or 00. These may be pronounced ‘false’ even where it would be ungrammatical for an adjective to appear in ordinary English.


In classical logic


In constructive logic



In linear logic

In linear logic, there is both additive falsity, denoted 00, and multiplicative falsity, denoted \bot. Despite the notation, it is 00 that is the bottom element of the lattice of linear truth values. (In particular, 00 \vdash \bot but 0\bot \nvdash 0.)

In a topos



In type theory

In type theory with propositions as types, falsehood is represented by the empty type.

In homotopy type theory

In homotopy type theory, falsehood is represented by the empty space.


In the topos SetSet




Last revised on December 10, 2017 at 18:52:04. See the history of this page for a list of all contributions to it.