Designing an Automated Theorem Prover

Abstract

Automated Theorem Proving (ATP) is a well developed technique and a powerful tool to deal with the theorem proving in mathematics such as propositional logic and First Order logic. It is a subfield of Automated Reasoning. This project implements an ATP for propositional logic. Satisfiability (SAT) ,which is a fundamental concept concerning interpretation in mathematic logic, is applied in the ATP. A formula of propositional logic is satisfiable if it is possible to find at least one solution to make the formula true. Two different implementations are created, namely, exhaustive search algorithm and Davis Putnam Logemann Loveland algorithm (DPLL). Experimental results indicate that the performance of DPLL is better at processing speed. The developed ATP is applied to solve N-Queens problem. A user interface and a new game are developed. The user is invited to solve the N-Queens problem and the computer uses ATP to check the move’s logical viability. It then informs the user whether his move is a feasible one.