PropLogic

PropLogic implements propositional logic in Ruby, usable like normal variables.

Installation

Add this line to your application's Gemfile:

gem 'prop_logic'

And then execute:

$ bundle

Or install it yourself as:

$ gem install prop_logic

Requirements

Using with CRuby, Version >= 2.0.0 is required. Doesn't work stably on 1.9.x due to unreliable behaviors on weak reference.

In JRuby and Rubinus it should work.

Usage

Overview

First, variables can be declared using PropLogic.new_variable. Next, it can be calculated using normal Ruby operators such as &, |, ~, and some methods. Finally, you can test satisfiability of these expressions.

# declartion
a = PropLogic.new_variable 'a'
b = PropLogic.new_variable 'b'
c = PropLogic.new_variable 'c'

# calculation
expr1 = (a & b) | c
expr2 = ~(a.then(b))
expr3 = expr1 | expr2

# conversion
nnf = expr3.to_nnf
cnf = expr3.to_cnf
sat = expr3.sat?

# comparement
diff = (~a | ~b).equiv?(~(a & b)) # true

# assignment
(a & b).assign_true(a).assign_false(b).reduce # PropLogic::False

Using normal Hash for caching

By default, prop_logic uses weak reference for caching terms, allowing garbage collection.

If this is inappropriate (overhead or unstability), use require 'prop_logic/hash_cache' to use Hash for caching.

Restriction

SAT solver bundled with this gem is brute-force solver (intended only for testing), so it is inappropriate to use for real-scale problems.

In CRuby and Rubinius, bindings to MiniSat (jkr2255/prop_logic-minisat) is available. It is a plugin for this gem, so no code (except require and Gemfile) needs to be changed to use prop_logic-minisat.

In JRuby binding to Sat4j (jkr2255/prop_logic-sat4j) is available.

References

PropLogic::Term is immutable, meaning that all calculations return new Terms.

PropLogic::Term instance methods

#and(*others), #&(*others)

calculate self & others[0] & others[1] & ....

#or(*others), #|(*others)

calculate self | others[0] | others[1] & ....

Warning for reducing with & / |

Because of immutability and internal system of and/or terms, many_terms.reduce(&:and) is exteremely slow. Use PropLogic.all_and/PropLogic.all_or or one_term.and(*others) to avoid this pitfall.

#not(),#~(), #-@()

calculate Not(self). #! is not present because it confuses Ruby behavior. (if present, !term is always truthy)

#then(other), #>>(other)

caslculate If self then other.

NNF

NNF doesn't contain following terms:

• If-then
• Negation of And/Or
• Double negation

#nnf? checks if the term is NNF, and #to_nnf returns term converted to NNF.

Reduction

Term is regarded as reduced if: 0. it is NNF 0. it contains no constants (PropLogic::True/PropLogic::False) 0. it contains no ambivalent terms 0. it contains no duplicated terms

#reduced? checks if the term is reduced, and #reduce returns reduced term.

Reduction

CNF is one of these:

1. Variable and its negation
2. Logical sum of multiple 1
3. Logical product of multiple (1 or 2)

#cnf? checks if the term is CNF, and #to_cnf returns terms converted to CNF (may use extra variables).

SAT judgement

#sat? returns:

• boolean false if unsatisfiable
• nil if satisfiability is undetermined
• One term satisfying original term if satisfiable

#unsat? returns true if unsatisfiable, false otherwise.

SAT enumrator

#each_sat is an enumerator for all satifiabilities. Returns Enumerator if calling without block.

PropLogic module methods

PropLogic.new_variable(name = nil)

declare new variable with name name. if name is not supplied, unique name is set.

Notice that even if the same name as before specified, it returns different variable.

PropLogic.all_and(*terms)/PropLogic.all_or(*terms)

calculate all and/or of terms. Use this when and/or calculation for many variables.

PropLogic.sat_solver/ PropLogic.sat_solver=`

set/get SAT solver object. It shoud have #call(term) method and return value is described in Term#sat?.

PropLogic.incremental_solver/ PropLogic.incremental_solver=`

set/get incremental SAT solver object. It shoud be class with #add and #sat? methods. (see DefaultIncrementalSolver for its interface)

Information

PropLogic::Term has some subclasses, but these classes are subject to change. Using subclasses of PropLogic::Term directly is not recommended.

Development

After checking out the repo, run bin/setup to install dependencies. Then, run bin/console for an interactive prompt that will allow you to experiment.

To install this gem onto your local machine, run bundle exec rake install. To release a new version, update the version number in version.rb, and then run bundle exec rake release to create a git tag for the version, push git commits and tags, and push the .gem file to rubygems.org.

Contributing

1. Fork it ( https://github.com/[my-github-username]/prop_logic/fork )
2. Create your feature branch (git checkout -b my-new-feature)
3. Commit your changes (git commit -am 'Add some feature')
4. Push to the branch (git push origin my-new-feature)
5. Create a new Pull Request

ToDo

• Introduce special blocks to build terms inside