Logic, Reasoning and Resolution Refutation

This critical thinking course explains how to apply logic and reasoning through resolution refutation. We begin by introducing you to various different logical languages and providing an overview of propositional calculus. We then lay out the symbols used in propositional calculus and show you how to convert English sentences into propositional calculus. We discuss predicate calculus (also called ‘first-order logic’) in detail and identify its symbols, semantics and differences to propositional calculus.

The course then examines various critical thinking techniques, including ‘modus ponens’, ‘modus tollens’, elimination, introduction and universal instantiation. We cover the unification and deduction process to help you apply logic to real-world scenarios. We demonstrate how to build a reasoning system and match two predicates to implement an inference engine. Since all variables need to be universally quantified, we explore the steps involved in the unification process and those taken to implement the resolution principle by deduction.

Our next section focuses on theorem proving by resolution refutation. We provide examples to help you understand the basic steps taken to establish theorems, including clause form, efficient resolution strategies and answer extraction from resolution refutation. The course examines unification substitution and Skolemization to enhance your practical critical reasoning skills. We also explain how to use Prolog, a logic programming language and an application of resolution theorem proving that is often used in modern computing. Our final section compares various reasoning approaches. This course suits computer programmers as it explains how critical thinking can be expressed and applied to enhance your computer science skills.