Logic: Language and Information 2

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.

This subject follows from Logic: Language and Information 1, to cover core techniques in first order predicate logic: the idea of formal languages with quantifiers, which gives us a way to talk about more logical structure than in propositional logic; and we will cover the central logical concepts such as consistency and validity; models; and proofs in predicate logic. But you won’t only learn these concepts and tools. We will also explore how these techniques connect with issues in linguistics, computer science, electronic engineering, mathematics, and philosophy.

Week 1. The Syntax of Predicate Logic; Translations using quantifiers

Week 2. Models for Predicate Logic; Classifying propositions and arguments; Finite and Infinite Domains

Week 3. Tree Proofs for Predicate Logic; Soundness and Completeness

Week 4. Identity; Functions; Counting 

Weeks 5–8. Applications to different reasoning domains (take at least three):

• Electronic Engineering — simplifying digital circuits with timing
  
• Philosophy — definite descriptions and existence
  
• Computer Science — databases, resolution and Prolog
  
• Linguistics — quantificational scope
• Mathematics — limits, continuity and quantifier alternation