# Course syllabus

## Course-PM

DAT060 / DIT202 Logic in Computer Science

LP1 HT21 (7.5 hp)

The course is offered by the department of Computer Science and Engineering.

### News

• Assignment 6 will contain 15 points instead of 10 so you have more opportunities to practice and get feedback!
• The exam will take place in an examination hall on campus.
It is then not allowed to have any help material but dictionaries to/from English.

### Contact Details

• Examiner and lecturer: Ana Bove <bove @ chalmers.se>
• Lecturer: Thierry Coquand <coquand @ chalmers.se>
• Teaching assistant:
• Jeremy Pope <popje @ chalmers.se>
• Nachiappan Valliappan <nacval @ chalmers.se>

### Course Purpose

Powerful tools for verifying software and hardware systems have been developed. These tools rely in a crucial way on logical techniques. This course provides a sound basis in logic and a short introduction to some logical frameworks used in modelling, specifying and verifying computer systems. A sound basic knowledge in logic is a welcome prerequisite for courses in program verification, formal methods and artificial intelligence.

### Schedule

See TimeEdit which is fully updated.
Course calendar is also updated where it comes to where the activity will take place.

#### Overview of Topics and Reading Material per Week

 Week Topics Reading Material/Book Sections 1 Recap logic, sets, relations, functions, induction sets relations functions notes on induction Structural induction 1.4.2 2 Natural deduction for propositional logic 1.1-1.3 3 Semantics of propositional logic, normal forms 1.4-1.5 except 1.4.2 4 Natural deduction and semantics for predicate logic 2.1-2.4 5 Undecidability of predicate logic and Post correspondence problemFixpoint and SAT solvingGuest lecture on applications of propositional and predicate logic. 2.5 6 Expressivity of predicate logic, compactness, Gödel's incompletness theoremLinear temporal logic 2.6, 3.2 7 LTL, CTL 3.2-3.5 8 Guest lecture on temporal logic.Algorithms, fix-point characterization Repetition, old exams 3.6-3.7

#### Exercises

Week 1: exercises1.pdf

Weeks 2--8: exercises2-8.pdf

### Course Literature

Logic in Computer Science by Michael Huth and Mark Ryan, second edition.

Exercises marked with an asterisk ("*") in the text book have solutions.

(There used to be an electronic version of the book available via Chalmers library, please check!)

### Course Design

The course consists of a series of lectures and exercise sessions.

The language of instruction is English.

### Changes Made since the Last Occasion

We will try to offer the two guest lectures that were offered last year to better show the applications of the course.
Our priority is to run the course as smooth as possible in what at the moment (June 2021) seems to be a hybrid way.

### Learning Objectives and Syllabus

After completing the course the student is expected to be able to:

Knowledge and understanding:

• explain when a given formula is a tautology,
• explain the notion of model of a first-order language and of temporal logic,
• explain when a first-order and a temporal logic formula is semantically valid,
• explain how to check if a branching-time temporal logic formula is valid in a given model,
• explain the meaning of the soundness and completeness theorems for propositional and predicate calculus.

Competence and skills:

• write and check proofs in natural deduction for propositional and predicate calculus,
• specify properties of a reactive system using linear-time temporal logic and branching time temporal logic.

Judgement and approach:

• judge the relevance of logical reasoning in computer science, i.e. for modelling computer systems,
• analyse the applicability of logical tools to solve problems in computer science, i.e. finding bugs with the use of model checking.

### Examination Form

OBS: The exam of the course will take place on an examination hall on campus.
It is then not allowed to have any help material but dictionaries to/from English.

The course is examined by an individual written exam taken place in an examination hall at the end of the course.

The exams has a maximum of 60 points and the passing grades in the exam are as follow:

Chalmers
 U: 0-29 3: 30-40 4: 41-50 5: 51-60
GU
 U: 0-29 G: 30-45 VG: 46-60

Note:

When making a natural deduction proof in the exam you are allowed to use any of the rules presented in page 27 of the book plus the introduction and elimination rules for both the universal and existential quantifiers, unless it is stated otherwise in an exercise.

In other words, you are allowed to use all introduction and elimination rules (including those for double negation) and the derived rules MT, PBC and LEM, unless stated otherwise.

No other result can be used unless it is proved.

Non-obligatory assignments:

There will be 6 non-obligatory individual assignments. The first five assignment gives up to ten points and the last one will give up to 15 points. 10% of those points count as bonus points in the written exam. These bonus points are valid for the whole academic year 21/22.

Solution to the assignments will be discussed in the Friday exercise session after the submission.

All submissions must include your name, and personal number and should be uploaded in Canvas. Your solutions must be clear and readable; everything must be carefully motivated!

As always in life, you should not cheat! Any suspicious on cheating will be taken seriously and must be reported to the Disciplinary Committee for further investigation.

Exam dates for 2021/2022: 25 Oct 2021 am, 3 Jan 2022 pm, 15 Aug 2022 pm.

### Course Evaluation

#### Student Representatives

CTH

Artur Marecos Mendes Leitao <marecos @ student.chalmers.se>
Johan Atterfors <atjohan @ student.chalmers.se>
Viktor Fredholm <vikfre @ student.chalmers.se>

GU

Benjamin Sannholm <gussannhbe @ student.gu.se>
Deeksha Gautam <gusgautde @ student.gu.se>
Filip Antonijevic <gusantfi @ student.gu.se>
Jan Simon Lindén <guslinsic @ student.gu.se>

#### Meetings

First meeting: September 16th, 17:00. Protocol.

Second meeting: October 14th, 15:15. Protocol.

Date Details Due