Trilean

An implementation of the K3+ three-valued logic. The third value in this library is Trilean.maybe() This is an extension of Kleene's strong logic of indeterminacy.

Three value logics allow reasoning in face of uncertainty. For example

iex> will_a_sea_battle_be_fought_tomorrow = Trilean.maybe()
...> nice_day_tomorrow = true
...>
...> _should_i_pack_a_picnic = (
...>   will_a_sea_battle_be_fought_tomorrow
...>   |> Trilean.and(nice_day_tomorrow)
...>   |> Trilean.possible?()
...> )
true

I should pack a picnic because it will be a nice day and there could be a spectacle to watch. (The sea battle problem is Aristotle's formulation of the contingent futures problem on which three value logics can shed some light.)

iex> will_a_sea_battle_be_fought_tomorrow = Trilean.maybe()
...> nice_day_tomorrow = false
...>
...> _should_i_pack_a_picnic = (
...>   will_a_sea_battle_be_fought_tomorrow
...>   |> Trilean.and(nice_day_tomorrow)
...>   |> Trilean.possible?()
...> )
false

I should not pack a picnic even though there could be a spectacle because it will be a crummy day.

All expressions evaluate the same as they would in normal boolean logic if their inputs are true or false. If, however, one or more of the inputs is :maybe then the output may become indeterminate. For example:

iex> Trilean.and(true, true)
true
iex> Trilean.and(true, false)
false
iex> Trilean.and(true, Trilean.maybe())
Trilean.maybe()

Operators

Operators for common uses are defined in Trilean.Operators

iex> use Trilean.Operators
...> will_a_sea_battle_be_fought_tomorrow = maybe()
...> nice_day_tomorrow = true
...>
...> _should_i_pack_a_picnic =
...>   (will_a_sea_battle_be_fought_tomorrow &&& nice_day_tomorrow)
...>   |> Trilean.possible?()
true

Supported operators are

• ~~~: Trilean.not/1
• |||: Trilean.or/2
• &&&: Trilean.and/2
• ~>: Trilean.implies/2
• <~>: Trilean.equivalence/2

Guards

Guards provided in Trilean.Guards.

iex> defmodule Picnic do
...>   use Trilean.Guards
...>   use Trilean.Operators
...>
...>  def pack_one?(sea_battle, nice_day) when is_possible(sea_battle),
...>    do: (sea_battle &&& nice_day) |> Trilean.possible?
...>  def pack_one(_,_), do:  false
...> end
...>
...> Picnic.pack_one?(Trilean.maybe(), true)
true

Installation

If available in Hex, the package can be installed by adding trilean to your list of dependencies in mix.exs:

def deps do
  [
    {:trilean, "~> 1.1.0"}
  ]
end

Documentation can be generated with ExDoc and published on HexDocs. Once published, the docs can be found at https://hexdocs.pm/trilean.