## MATH2041 Logic

### 10 creditsClass Size: 120

Module manager: Dr Andrew Brooke-Taylor
Email: a.d.brooke-taylor@leeds.ac.uk

Taught: Semester 2 (Jan to Jun) View Timetable

Year running 2020/21

### Pre-requisite qualifications

Familiarity with proof by mathematical induction.
Interest in abstract, mathematical proof writing.

### This module is mutually exclusive with

 MATH2042 Logic with Computation PHIL2122 Formal Logic

Module replaces

MATH2040 Mathematical Logic 1

This module is approved as a discovery module

### Module summary

This module is an introduction to mathematical logic introducing formal languages that can be used to express mathematical ideas and arguments. It throws light on mathematics itself, because it can be applied to problems in philosophy, linguistics, computer science and other areas.

### Objectives

On completion of this module, students should be able...
1. To describe the fundamental notions of mathematical logic, including the distinction between syntax and semantics.
2. To present a proof of the completeness theorem in the propositional case and introduce a first order predicate calculus.

Learning outcomes
1. To express logical arguments in a formal language and thereby to analyse their correctness.
2. To distinguish between syntax and semantics, and give simple formal proofs in a natural deduction system.
3. To give a proof by induction on a finite tree.
4. To apply the soundness and completeness theorems to establish whether a formula is derivable from a set of axioms or not.

### Syllabus

1. Propositional Logic. Syntax. Semantics. Satisfiability, tautologies, contradictions. Disjunctive and conjunctive normal forms. A formal proof system. Completeness and compactness.
2. Boolean algebras and partially ordered sets.
3. Predicate Logic. Language and syntax. First-order structures. Truth in a structure. Prenex normal form. A formal proof system.

### Teaching methods

Due to COVID-19, teaching and assessment activities are being kept under review - see module enrolment pages for information

 Delivery type Number Length hours Student hours Workshop 10 1.00 10.00 Lecture 11 1.00 11.00 Private study hours 79.00 Total Contact hours 21.00 Total hours (100hr per 10 credits) 100.00

### Private study

Studying and revising of course material.
Completing of assignments and assessments.

### Opportunities for Formative Feedback

Regular problem solving assignments.

### Methods of assessment

Due to COVID-19, teaching and assessment activities are being kept under review - see module enrolment pages for information

Coursework
 Assessment type Notes % of formal assessment In-course Assessment . 15.00 Total percentage (Assessment Coursework) 15.00

There is no resit available for the coursework component of this module. If the module is failed, the coursework mark will be carried forward and added to the resit exam mark with the same weighting as listed above.

Exams
 Exam type Exam duration % of formal assessment Open Book exam 2 hr 00 mins 85.00 Total percentage (Assessment Exams) 85.00

Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated