logical
A Ruby implementation of some mathematical logic concepts and algorithms.
It makes no attempts to be computationally efficient, it strives to be handy instead.
Setup
logical is built as a gem for Ruby apps, but if you just wish to execute it in an interactive session there's a convenience standalone Docker image available.
As a gem
Add:
gem 'logical'
to your application's Gemfile or run:
gem install logical
(See RubyGems)
As a docker container
Requires Docker.
Clone the repository and run:
docker build -t logical .
docker run -it logical
Usage
Require the gem:
require 'logical'
Include the module:
include 'Logical'
Parse a formula:
f = NaiveParser.parse('((p∧q)→r)')
NaiveParser requires formulas to be enclosed within parentheses (i.e
(p∧q), notp∧q).
Alternatively, build a formula:
p = Literal.new(:p)
q = Literal.new(:q)
r = Literal.new(:r)
f = Implication.new(Conjunction.new(p, q), r)
Serialize it:
f.to_s # '((p∧q)→r)'
Get its rank:
f.rank # => 2
Check for equality (not equivalence):
f == p # => false
f == f # => true
Build a truth table for it and print it:
t = TruthTable.new(f)
puts t.evaluations.map(&:to_s)
Output:
{"p"=>true, "q"=>true, "r"=>true} ⇒ ((p∧q)→r) = true
{"p"=>true, "q"=>true, "r"=>false} ⇒ ((p∧q)→r) = false
{"p"=>true, "q"=>false, "r"=>true} ⇒ ((p∧q)→r) = true
{"p"=>true, "q"=>false, "r"=>false} ⇒ ((p∧q)→r) = true
{"p"=>false, "q"=>true, "r"=>true} ⇒ ((p∧q)→r) = true
{"p"=>false, "q"=>true, "r"=>false} ⇒ ((p∧q)→r) = true
{"p"=>false, "q"=>false, "r"=>true} ⇒ ((p∧q)→r) = true
{"p"=>false, "q"=>false, "r"=>false} ⇒ ((p∧q)→r) = true
Get some info:
t.valid? # false
t.satisfied? # true
t.invalid? # false
Contributing
Setup
Build the Docker development image:
docker build -f Dockerfile.dev -t logical-dev .
Launch a Docker container mounting the project directory:
docker run --name=logical-dev -d --mount type=bind,src=${PWD},target=/var/app logical-dev
Implement your changes.
Executing Tests
Launch Rake within the Docker container bash shell:
docker exec -ti logical-dev bash -c rake
License
logical is released under the MIT License.