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2020/21 Undergraduate Module Catalogue

MATH2042 Logic with Computation

15 creditsClass Size: 160

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-requisites

MATH2920

Computational Mathematics

This module is mutually exclusive with

MATH2041	Logic
PHIL2122	Formal Logic

Module replaces

MATH2040 Mathematical Logic 1

This module is not approved as a discovery module

Module summary

Logic is the study of reasoning itself. Since its origins in ancient Greece, logic has evolved into a wide and vibrant subject, with many important applications to other areas of mathematics and to computer science. A typical application in mathematics is to decide whether a certain statement can be proved from a given set of axioms (e.g. whether the axiom on parallel lines follows from Euclid’s other axioms). In computer science, ever since the pioneering work of Turing, logic has played a fundamental role in describing and analysing algorithms. The module will provide an introduction to logic, with emphasis on its computational applications.

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.
3. To describe the fundamental notions of Computational Logic, including algorithmic proof verification.

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.
5. To understand the working of fundamental algorithms in computational logic.

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.
4. Data-types for propositional logic. Algorithms for checking well-formed formulas. Algorithms for constructing parse trees. Algorithms for satisfiability. Construction of formal natural deduction proofs for propositional logic in software.Algorithms for proof-checking.
5. Formal manipulations of Boolean algebras in software.
6. Data-types for first-order formulas and natural deduction proofs for first-order logic. Construction of formal natural deduction proofs for first order logic in software. Algorithms for proof-checking.

Teaching methods

Delivery type	Number	Length hours	Student hours
Workshop	10	1.00	10.00
Class tests, exams and assessment	1	2.00	2.00
Lecture	11	1.00	11.00
Practical	5	2.00	10.00
Tutorial	5	1.00	5.00
Private study hours			112.00
Total Contact hours			38.00
Total hours (100hr per 10 credits)			150.00

Private study

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

Opportunities for Formative Feedback

Regular problem-solving assignments.

Methods of assessment

Coursework

Assessment type	Notes	% of formal assessment
Computer Exercise	.	30.00
In-course Assessment	.	10.00
Total percentage (Assessment Coursework)		40.00

In order to pass the module, students must pass the MATH2041 component (which is at least 40% on exam and in-course assessment combined) and score at least 40% on the Computer Exercises.

Exams

Exam type	Exam duration	% of formal assessment
Open Book exam	2 hr 00 mins	60.00
Total percentage (Assessment Exams)		60.00

Students who have failed the MATH2041 component will need to resit the exam; students who have failed the computer exercises will need to resubmit these. There is no resit available for the 10% in-course assessment component of this module. If the module is failed, the mark for this component will be carried forward and added to the resit exam and/or computer exercises mark with the same weighting as listed above.

Reading list

There is no reading list for this module

Last updated: 10/08/2020 08:42:06

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