Introductory description

PH210 Logic II: Metatheory

Module aims

Outline syllabus

This is an indicative module outline only to give an indication of the sort of topics that may be covered. Actual sessions held may differ.

• Week 1: introduction, set theory, inductive definitions
• Week 2: syntax and semantics of propositional logic
• Week 3: natural deduction
• Week 4: soundness of propositional logic
• Week 5: completeness of propositional logic
• Week 7: syntax and semantics of first-order logic
• Week 8: natural deduction and soundness for first-order logic
• Week 9: completeness for first-order logic
• Week 10: the compactness Theorem and applications

Learning outcomes

By the end of the module, students should be able to:

• demonstrate knowledge of the Soundness and Completeness Theorems for propositional and first-order logic and related technical results and definitions (subject knowledge and understanding)
• understand the significance these concepts and results have for logic and mathematics (cognitive skills)
• use and define concepts with precision, both within formal and discursive contexts (key skills)
• write precise mathematical proofs (subject specific skills)

Indicative reading list

Our primary text will be

• Logic and Structure, 5th edition by Dirk van Dalen, Springer Verlag, 2013

in which we will cover most of chapters 1-4. The whole book is available electronically through the library via the above link.

The same material is also covered at a more elementary level in chapters 15-19 of

• Language, Proof and Logic, Jon Barwise and John Etchemendy, CSLI Publications, 2002.

Students lacking a background in elementary discrete maths (e.g. basic set theory and mathematical induction) are encouraged to obtain

• How to prove It: A Structured Approach, Daniel J. Velleman, Cambridge University Press, 2006.

View reading list on Talis Aspire

Subject specific skills

Demonstrate knowledge of the Soundness and Completeness Theorems for propositional and first-order logic and related technical results and definitions
Understand the significance these concepts and results have for logic and mathematics
Use and define concepts with precision, both within formal and discursive contexts

Transferable skills

Understand definitions and proof techniques from metalogic applicable in other domains -- e.g. such as mathematical and structural induction, basic set theoretic operations and constructions
The ability to comprehend and construct precise mathematical proofs"