The Importance of Being Formal
Brief Description
Brief Description
Formal methods of reasoning have been studied in all major civilizations, but the appearance of automatic computing devices in the 20th century has led to an explosion of interest in and applications of formal logic. Today, the advantages of formal reasoning are recognized and utilized far beyond computer science. Students of this module will discover the power as well as the limitations of formal methods for philosophy and mathematics, and learn to apply them in diverse areas. Each student will investigate one of these areas in depth, leading to an essay and presentation.
Covered Topics
Topics Covered
Introduction (Week 1)
Part I: Foundations (Weeks 2-5)
- Traditional logic as a formal language (syllogisms, medieval logic)
- Syntax and semantics, deduction
- Propositional logic
- Formal languages and their processing
- Natural languages vs artificial languages
- Programming and reasoning languages
- Practical sessions:
- Solving Lewis Carroll puzzles using the proof assistant Coq
- Computer assisted deduction in propositional logic
- Applications:
- Political speeches
- Automated scheduling using formal logic
Part II: Predicate Logic (Weeks 6-9)
- Syntax, semantics, deduction
- Practical session:
- Computer-assisted deduction in predicate logic
- Applications:
- Logical fallacies and how to avoid them using a formal approach
Material
Material
The module material (notes, slides, software) will be made available in this space.
| Lecture | Date | Subject | Slides | Notes and Hand-outs | Additional Material |
| Week 1 | 16/1 | Introduction to UIT2206 | Slides in color,Slides in b/w (for printing) | Naming and Necessity, Lecture I, Saul Kripke; read and discuss in Forum before Lecture Week 2 | No tutorials; they start on 24/1 |
| Week 2 | 23/1 | Traditional Logic | Slides in color,Slides in b/w (for printing) | Week 2: Traditional Logic I Coq script Coq installer for Windows Coq installer for Mac |
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| Week 3 | 29/1 | Traditional Logic II | Slides in color,Slides in b/w (for printing) | Week 3: Traditional Logic II Coq script Cheat sheet |
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| Week 4 | 5/2 | Propositional Logic I | Slides in color,Slides in b/w (for printing) | Week 3: Traditional Logic II Coq script Cheat sheet |
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| Week 5 | 12/2 | Propositional Logic II | Slides in color,Slides in b/w (for printing) | see Week 4 | - |
| Week 6 | 19/2 | Predicate Logic I | Slides in color,Slides in b/w (for printing) | Week 6: Predicate Logic | Coq script for traditional logic using predicate logic. Cheat sheet |
| Week 7 | 5/3 | Predicate Logic II | Slides in color,Slides in b/w (for printing) | - | Coq script for Week 7 |
| Week 8 | 12/3 | Ugly corners | Slides in color,Slides in b/w (for printing) | - | Midterm preparation exercises solution (except first three questions) |
| Week 9 | 19/3 | Midterm; Modal Logic | Midterm, Slides in color,Slides in b/w (for printing) |
Week 9: Modal Logic | - |
| Week 10 | 26/3 | Gödel's incompleteness results | Slides in color,Slides in b/w (for printing) | Reading material: Mumon and Gödel, Chapter IX of "Gödel, Escher, Bach" by Douglas Hofstadter (copy available at USP admin office, front desk) |
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Assignments
Assignments and Lab Tasks
Assignments are distributed online in this section. Submission as indicated in the assignments. The solutions are discussed in the tutorial session after submission, see calendar above.
| Assignment | Date handed out | Time due | Assignment Solution |
| Assignment Week 4 | 7/2 | 11/2, 23:59 | - |
| Assignment Week 7 | 7/3 | 12/3, 23:59 | - |
Student Essays and Presentations
Student Essays and Presentations
Every student of UIT2206 will prepare an essay and a presentation. The essays are submitted in three stages: A proposal is due on Week 5 A draft will be submitted by Week 9, and the final version is due by Week 13. The draft and final submission are preceded by an appointment to the USP Writing Centre. The director of the Writing Centre, A/P Don Favareau and the lecturer of UIT2206, A/P Martin Henz, worked out a Writing Guide for UIT2206, which is highly recommended reading as it specifies the lecturer's expectations for the essays. These guidelines are also distributed to the Writing Assistants of the Writing Centre, who use them as a reference for assisting the students of UIT2206.
The presentations are given in Weeks 11, 12 and 13 during the Friday sessions, and Lecture slots.
Other Module Information
Other Module Information
Modular credits: 4
Status: Elective module for USP students
Assessment (approximate numbers): All assessment for the module is individual; there are no group components.
- Class participation: 10%
- Tutorial participation: 10%
- Assignments: 20%
- Test (Week 9 or 10): 20%
- Presentation (Weeks 10 to 13): 20%
- Report: 20%
Lectures
- 13 sessions, 2 hrs/wk, time: Wednesday 10 - 12 am, venue: SR1
- first lecture: 16/1/2013 see module calendar and official NUS Academic Calendar
Tutorials
- 2 hr/wk
- Venue: USP SR2
- Times:
- Group 1: Fridays, 8am-10am
- Group 2: Fridays, 10am-12noon
Textbook
There is no textbook. The notes provided for each lecture make up the module material. Books for additional reading will be recommended from time to time.
Assignments and labs quizzes
Assignments will be given out each week on this module page. Assignment scores make up about 20% of the overall marks.
Discussion group:
An IVLE discussion forum will be set up for UIT2206. There is a topic in the main forum for every chapter of the module notes, as well as forums for anonymous feedback and discussing administrative matters such as exams.
Announcements
Announcements are distributed using the IVLE Announcement feature.
Test
There will be a test, covering the formal logic part of the module. The test will take place during lecture time; details to be announced.