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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 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?
* Is this information belong to in my 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.
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 in propositional and predicate logic. But you won't just learn concepts and tools. We will also explore how these techniques connect with problems in linguistics, computer science, electronic engineering, mathematics and philosophy.
Intended learning outcomes
Students who successfully complete this subject will:
- develop and demonstrate and understanding of the core features of propositional and predicate logic, including translating into and out of the formal languages; manipulating models and proof trees, and using these to make simple judgements concerning validity, consistency, equivalence, etc.;
- develop a command of the different ways formal logic can be applied in problems in computer science, digital systems, linguistics, mathematics and philosophy;
- work in groups to clarify problems, apply reasoning techniques to different issues, and to critically evaluate the results;
- construct arguments and answer questions, bringing together both formal and informal reasoning techniques—to clarify issues, analyse options and propose solutions.
Last updated: 9 September 2021