Propose is a playground for creating, manipulating, and verifying statements in propositional logic.
It comes with a simple command-line REPL
propose, which can answer questions about propositional statements.
Ruby 2.4+
gem install proposeYou can write formulas with Propose in plain English (e.g. p or q), or
use the standard propositional calculus notation (e.g. p ∨ q), amongst a few
other options outlined below.
Atoms are the basic unit of propositional logic, and represent a single statement which can be true or false, like "The sun is shining." They can be written in one or more lowercase letters.
> p
> q
> ball
The negation of an atom expresses that the statement is not true. Negation can also be applied to larger expressions.
> not p
> ¬p
> !p
The conjunction of two expressions denotes that both expressions are true.
> p and q
> p ∧ q
> p & q
The disjunction of two expressions denotes that at least one of the expressions is true.
> p or q
> p ∨ q
> p | q
Implication expresses the concept that the expression on the right is a logical consequence of the expression on the left, e.g. "if the sun is shining, then the ice is melting".
> p implies q
> p imply q
> p → q
> p -> q
> p => q
You can write arbitrarily complex formulas by using parentheses to nest expressions.
> p or (q and r)
> (p or q) implies (q or r)
> not (p and q)
For convenience, you can avoid writing unnecessary parentheses by adhering to the conventions below:
- ¬ binds more tightly than ∧, meaning ¬p ∧ q denotes (¬p) ∧ q
- ∧ binds more tightly than ∨, meaning p ∧ q ∨ r denotes (p ∧ q) ∨ r
- ∨ binds more tightly than →, meaning p ∨ q → q ∨ r denotes (p ∨ q) → (q ∨ r)
- → is right-associative, meaning p → q → r denotes p → (q → r)
To print out a truth table for a propositional formula, simply enter the formula as a command.
> not p or q and r
+---+---+---+--------+
| ¬p ∨ (q ∧ r) |
+---+---+---+--------+
| p | q | r | Result |
+---+---+---+--------+
| T | T | T | T |
| F | T | T | T |
| T | F | T | F |
| F | F | T | T |
| T | T | F | F |
| F | T | F | T |
| T | F | F | F |
| F | F | F | T |
+---+---+---+--------+
This project is released under the MIT license.