https://github.com/thedivic/gilmore-algorithm

This is my implementation of the Gilmore's algorithm. It is the first Herbrand universe based algorithm for proving the unsatisfiability of first order logic formulas.
https://github.com/thedivic/gilmore-algorithm

Last synced: 21 days ago
JSON representation

This is my implementation of the Gilmore's algorithm. It is the first Herbrand universe based algorithm for proving the unsatisfiability of first order logic formulas.

• Host: GitHub
• URL: https://github.com/thedivic/gilmore-algorithm
• Owner: TheDivic
• Created: 2014-08-11T22:35:14.000Z (over 10 years ago)
• Default Branch: master
• Last Pushed: 2015-09-30T15:34:36.000Z (over 9 years ago)
• Last Synced: 2024-11-12T14:07:39.519Z (3 months ago)
• Language: Python
• Homepage:
• Size: 211 KB
• Stars: 0
• Watchers: 2
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md

Awesome Lists containing this project

README

        
#Gilmore's algorithm

Gilmore's algorithm is based on a fact that the problem of satisfiability of formulas in

first order logic is semi-decidable, if a formula is unsatisfiable there is a decision procedure that will prove it's unsatisfiability.

If *S(i)* is the set of ground clauses obtained by replacing the variables in formula *S* with the constants in the i-th level constant

set of the [Herbrand Universe](http://mathworld.wolfram.com/HerbrandUniverse.html), then all of the elements of *S(i)* must be satisfiable in order for the starting formula *S* to be satisfiable.

Gilmore's algorithm uses the multiplication method to find an unsatisfiable element of *S(i)*. It is not guarateed that the algorithm will find the proof.