orgtt.el

Creating truth tables is boring, especially when you get more than 2 or 3 variables. They're easy and mechanical but it can be easy to make still mistakes. Wait! That sounds perfect for automation!

orgtt.el automates the creating of truth tables from a given formula. It creates the org table for you with all possible valuations already inserted. It provides two functions for you to call interactively, orgtt-create-table and orgtt-create-table-and-solve (WIP).

orgtt-create-table

orgtt-create-table will prompt you to enter a formula (e.g. A + B) and it will insert an org table with rows for all of the possible valuations for the variables filled in. Like the one below.

| A   | B   | A + B |
|-----+-----+-------|
| nil | nil |       |
| nil | t   |       |
| t   | nil |       |
| t   | t   |       |

You can easily define a table formula to fill in the column for the formula based by adding #+TBLFM: $3='(or (intern $1) (intern $2)) where intern is a built-in emacs functions which turns the string "nil" into nil and the string "t" into t. You can evaluate this formula by placing your cursor over it and pressing C-c C-c giving you the table below.

| A   | B   | A + B |
|-----+-----+-------|
| nil | nil | nil   |
| nil | t   | t     |
| t   | nil | t     |
| t   | t   | t     |
#+TBLFM: $3='(or (intern $1) (intern $2))

orgtt-create-table-and-solve

This is currently a work in progress

As with orgtt-create-table, orgtt-create-table-and-solve will prompt you for a formula. The difference is that it will not only give you a table with all the valuations for the given formula, it will give you a table including the evaluation of the formula. Like in the example of the second table above.

The formula syntax you can use is defined in orgtt-connective-alist and you can change it by adding or removing things but by default you are able to use to following syntax in your formulas:

Syntax	Meaning
-	Negation
.	Logical and
+	Logical or
->	Material implication
<->	Biimplication
<+>	Exclusive or

Options

You can customise aspects of orgtt.el to suit your needs and preferences.

orgtt-connective-alist

This is an alist mapping connectives to their functionality. By default it is:

'(("-"   . orgtt--negate)
  ("+"   . orgtt--lor)
	("."   . orgtt--land)
	("->"  . orgtt--implication)
	("<->" . orgtt--biimplication)
	("<+>" . orgtt--xor))

It effects how the input formula in orgtt-create-table-and-solve is converted into a formula usable by orgtbl.

You can extend the list of usable connectives by adding to this list. For the sake of simplicity, only unary and binary connectives are allowed.

orgtt-use-binary

By giving orgtt-use-binary a truthy value, your tables will use 0 instead of nil and 1 instead of t. Like in the table below.

| A | B | A + B |
|---+---+-------|
| 0 | 0 |       |
| 0 | 1 |       |
| 1 | 0 |       |
| 1 | 1 |       |

This could easily be extended to map t and nil to some string to you could customise however you want.