Exam (elaborations)
COS3761_ASSIGNMENT_3_SEMESTER_2_2023
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Tutorial Letter 101/3/2023Formal Logic III
COS3761
Semesters 1 and 2
School of Computing
, COS3761/101/3/2020
CONTENTS
Page
1 INTRODUCTION AND WELCOME .............................................................................................. 3
2 PURPOSE AND OUTCOMES OF THE MODULE ........................................................................ 3
2.1 Purpose ........................................................................................................................................ 3
2.2 Outcomes ..................................................................................................................................... 4
3 LECTURER AND CONTACT DETAILS ....................................................................................... 5
3.1 Lecturers ....................................................................................................................................... 5
3.2 Department ................................................................................................................................... 5
3.3 University ...................................................................................................................................... 6
4 MODULE RELATED RESOURCES ............................................................................................. 6
4.1 Tutorial matter ............................................................................................................................... 6
4.2 Prescribed book ............................................................................................................................ 6
4.3 Learning units on myUnisa ............................................................................................................ 7
4.4 MO001 tutorial letter ..................................................................................................................... 7
5 STUDENT SUPPORT SERVICES FOR THE MODULE ............................................................... 7
5.1 Students who have limited access to the internet .......................................................................... 7
6 MODULE SPECIFIC STUDY PLAN ............................................................................................. 8
7 ASSESSMENT ............................................................................................................................. 8
7.1 Assessment plan ........................................................................................................................... 8
7.2 Assignment numbers .................................................................................................................... 8
7.3 Due dates ..................................................................................................................................... 8
7.4 Submission of assignments........................................................................................................... 9
8 ASSIGNMENTS .......................................................................................................................... 10
8.1 Assignments for the first semester .............................................................................................. 10
8.2 Assignments for the second semester ........................................................................................ 38
9 EXAMINATIONS ........................................................................................................................ 66
10 CONCLUSION ............................................................................................................................ 66
2
, COS3761/101/3/2020
1 INTRODUCTION AND WELCOME
Dear Student
We would like to welcome you to COS3761 and hope that you will find this module, as well as your online
learning experience, interesting and rewarding. We will do our best to make your study of this module
successful, and recommend that you start studying early in the semester and resolve to do all the
assignments to the best of your ability.
Do not hesitate to contact your lecturer (by email or by telephone) if you are experiencing problems with
the content of this tutorial letter or any aspect of the module. I sincerely hope that you find this module, as
well as your online learning experience interesting and rewarding and trust that you will complete the
module successfully.
Because this is a fully online module, you need to use myUnisa to study and complete the learning
activities for this course. It is imperative that you work through the Learning units on the website.
You need to visit the websites on myUnisa for COS3761 frequently. The website for your module is:
COS3761-20-S1 for the first semester
or
COS3761-20-S2 for the second semester.
1.1 Getting started …
Owing to the nature of this module, you can read about the module and find your study material online. Go
to the website at https://my.unisa.ac.za and log in using your student number and password. You will see
[COS3761-2020] in the row of modules displayed in the orange blocks at the top of the webpage. Select the
More tab if you cannot find the module you require in the blocks displayed. Then click on the module you
want to open.
We wish you much success in your studies!
2 PURPOSE AND OUTCOMES OF THE MODULE
2.1 Purpose
The purpose of studying logic is to refine one’s natural ability to reason and argue. Logic is concerned with
training the mind to think clearly. The aim of logic is to obtain clarity in the definition and arrangement of
our ideas and other mental images, consistency in our judgements, and validity in our processes of
inference. Logic is about representing knowledge in a precise language so that a computer can reason about
it, i.e. so that an algorithm can be defined to make valid deductions from the knowledge. Logic is applied
extensively in the fields of Artificial Intelligence, Computer Science and Philosophy, and this module aims
to provide a solid foundation for these studies.
3
, COS3761/101/3/2020
2.2 Outcomes
At the end of this module you should have obtained strategies for thinking effectively, know about the
common errors in reasoning which should be avoided and have developed effective techniques for
evaluating arguments. You should know some of the logic languages used to represent knowledge, and
understand some of the computer algorithms used to reason about the knowledge represented in such
languages.
Specific outcomes Assessment criteria
Logical connectives are used to combine given
names and predicates correctly to translate given
English sentences into sentences of propositional or
predicate logic;
Logical connectives and symbols are interpreted
Construct and interpret propositional correctly to translate given propositional or
1
and predicate logic sentences. predicate logic sentences into English sentences;
The parse tree of a given predicate logic formula is
constructed and all its sub formulas are listed
correctly;
Correct substitution of variables of a predicate
logic formula is done.
A model where a given propositional logic,
predicate logic or basic modal logic sentence is true
or false is constructed;
A propositional, predicate or basic modal logic
Construct models and sentences to sentence that is true or false in a given model is
demonstrate understanding of the constructed;
2
semantics of propositional logic, A propositional, predicate or basic modal logic
predicate logic and basic modal logic. model where an entailment relation does not hold is
constructed;
A propositional, predicate or basic modal logic
model showing that a given sequent is not provable
is constructed.
A proof by mathematical induction of some
theorem is given;
Give formal proofs of “sequents” in The rules of Natural Deduction are used to
3 propositional logic, predicate logic or construct formal proofs of sequents in propositional
basic modal logic. logic or predicate logic where every line of the
proofs consists of a First-order Logic sentence
following on the previous line(s) while citing the
applicable rule;
4
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