https://github.com/nsajko/twoelementbooleanalgebra.jl

Simplest non-trivial Boolean algebra, the two-element Boolean algebra
https://github.com/nsajko/twoelementbooleanalgebra.jl

boolean boolean-algebra boolean-logic logic logical-operators

Last synced: 4 months ago
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Simplest non-trivial Boolean algebra, the two-element Boolean algebra

• Host: GitHub
• URL: https://github.com/nsajko/twoelementbooleanalgebra.jl
• Owner: nsajko
• License: mit
• Created: 2025-10-01T18:39:34.000Z (4 months ago)
• Default Branch: main
• Last Pushed: 2025-10-03T16:47:10.000Z (4 months ago)
• Last Synced: 2025-10-03T18:40:07.701Z (4 months ago)
• Topics: boolean, boolean-algebra, boolean-logic, logic, logical-operators
• Language: Julia
• Homepage:
• Size: 22.5 KB
• Stars: 1
• Watchers: 1
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md
  • License: LICENSE

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README

          
# TwoElementBooleanAlgebra

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A software package for the Julia programming language implementing the simplest non-trivial Boolean algebra, the two-element Boolean algebra.

The only public binding is the type, `Boole`. It is different from `Bool` in that `one(Boole) + one(Boole)` equals one instead of two.

## Usage example

```julia-repl

julia> using TwoElementBooleanAlgebra

julia> Boole(0)

Boole(0)

julia> Boole(0) + Boole(0)

Boole(0)

julia> Boole(0) + Boole(1)

Boole(1)

julia> Boole(1) + Boole(1)

Boole(1)

julia> Boole(0) * Boole(1)

Boole(0)

julia> !Boole(0)

Boole(1)

```

## An application: represent a relation with a logical array

A logical array represents a mathematical relation. Specifically, an `X::AbstractMatrix{Boole}` represents a binary relation. Then:

* matrix addition (`X + Y`) corresponds to relation union

* pointwise multiplication (`X .* Y`) of matrices corresponds to relation intersection

* matrix multiplication (`X * Y`) corresponds to relation composition

* matrix transpose (`transpose(X)`) or adjoint (`adjoint(X)` or `X'`) results in the converse relation

* pointwise negation (`(!).(X)`) results in the complementary relation

* pointwise partial order (`all(splat(≤), zip(X, Y))`) corresponds to the subset/inclusion predicate