Logic: Language and Information 1

This is an introduction to formal logic and how it is applied in computer science, electronic engineering, linguistics and philosophy. You will learn propositional logic—its language, interpretations and proofs, and apply it to solve problems in a wide range of disciplines.

Course at a Glance

Information is everywhere: in our words and our world, our thoughts and our theories, our devices and our databases. Logic is the study of that information: the features it has, how it’s represented, and how we can manipulate it. Learning logic helps you formulate and answer many different questions about information:

• Does this hypothesis clash with the evidence we have or is it consistent with the evidence?
• Is this argument watertight, or do we need to add more to make the conclusion to really follow from the premises?
• Do these two sentences say the same things in different ways, or do they say something subtly different?
• Does this information follow from what’s in this database, and what procedure could we use to get the answer quickly?
• Is there a more cost-effective design for this digital circuit? And how can we specify what the circuit is meant to do so we could check that this design does what we want?
These are questions about Logic. When you learn logic you'll learn to recognise patterns of information and the way it can be represented. These skills are used whether we're dealing with theories, databases, digital circuits, meaning in language, or mathematical reasoning, and they will be used in the future in ways we haven't yet imagined. Learning logic is a central part of learning to think well, and this course will help you learn logic and how you can apply it.

If you take this subject, you will learn how to use the core tools in logic: the idea of a formal language, which gives us a way to talk about logical structure; and we'll introduce and explain the central logical concepts such as consistency and validity; models; and proofs. But you won’t only learn concepts and tools. We will also explore how these techniques connect with issues in linguistics, computer science, electronic engineering, and philosophy.

Course Syllabus

Week 1The Syntax of Propositional Logic; Truth Tables; Classifying Propositions

Week 2. Relationships between Propositions; Tree Proofs; Soundness and Completeness

Weeks 3–5. Applications to different reasoning domains (take at least two):

• Electronic Engineering — simplifying digital circuits
• Philosophy — vagueness and borderline cases
• Computer Science — databases, resolution and propositional Prolog
• Linguistics — meaning: implication vs implicature

Recommended Background

This subject presumes no specialist background knowledge. You just need to be able to read and write, and be prepared to think, work and learn new skills—in particular, a willingness to work with symbolic representation and reasoning.

The course is self contained, with all required resources available online.

The textbook Logic (Greg Restall, Routledge 2000; especially chapters 1 to 5) covers most but not all of the material in this course. If you like following along with a book, this one will suit the course, but it is complementary and not necessary. We will provide you with a comprehensive set of written course notes, as well as the lecture videos and other freely available teaching resources.

Course Format

The class will consist of lecture videos, which are between 5 and 15 minutes in length. They will contain integrated quiz questions to give you immediate feedback. There will be practice problems available for your to sharpen your skills, and grading problems to form a part of your final grade. In weeks 3-5 there are four topics, from which each student is expected to choose at least two. These will be assessed by a combination of quizzes and short assignments. There is a final exam to wrap everything up.

FAQ

• Will I get a Statement of Accomplishment after completing this class?

Yes. Students who successfully complete the class will receive a Statement of Accomplishment signed by the instructors.

• What resources will I need for this class?

For this course, all you need is an Internet connection, and the time to watch the lectures, read the notes, practice your skills, think, and discuss the material online with other people participating in the class.

• What if I love this subject and I want to learn more logic?

Immediately after Logic 1, we’re be teaching Logic: Language and Information 2, and introduction to first order predicate logic and its connections to computer science, electronic engineering, linguistics, mathematics and philosophy.