A. Propositional logic - Syntax and semantics - Informal mathematical argumentation - Application: Paradoxes and problem solving - Boolean algebra - Formal proof methods: Natural deduction, resolution - Soundness, completeness and decidability
B. Predicate logic - Syntax and semantics - Proof methods: Natural deductio - Completeness and decidability: Gödel's theorems - Application: Program verification
C. First order theories - Theories and axiomatisation - Application: Algebraic data types
D. Proof by induction - Well-founded induction - Inductive definitions and structural induction - Co-induction
E. Modal and temporal logic - Syntax and semantics: Kripke structures - Proof methods: Model checking - Application: Parallel processes
Intended learning outcomes *
The overall aim of the course is to expose the students to mathematical logic and its use within theoretical computer science. The main focus of the course is on mastering the various proof techniques needed in other courses later in the curriculum.
After the course, the successful student will be able to: - express informal statements in propositional and first-order predicate logic, - argue for the correctness of a given proof calculus by relating appropriately its syntax and semantics, - apply natural deduction for proving statements in first-order predicate logic, - axiomatize abstract data types, - perform proofs by well-founded and structural induction, - perform proofs by co-induction, - perform simple verifications based on temporal logic.
Lecutres: 30 h Tutorials: 14 h Laboratory assignments: 8 h
Literature and preparations
Specific prerequisites *
For single course students: completed upper secondary education including documented proficiency in Swedish corresponding to Swedish B, English corresponding to English A. Furthermore: 7,5 hp in mathematics and 6 hp in computer science or programming technics.
For those already studying at KTH: DD1340 Introduction to Computer Science. At least two of the courses SF1612 Mathematic, Basic Course, SF1625 Calculus in One Variable and SF1604 Linear Algebra. Furthermore we recommend DD1361 Programming Paradigms (can be taken at the same time as this course).
No information inserted
The course literature is announced at least 4 weeks before the course starts at course web page.
Examination and completion
If the course is discontinued, students may request to be examined during the following two academic years.
Grading scale *
A, B, C, D, E, FX, F
Grading scale: P, F
Grading scale: A, B, C, D, E, FX, F
Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.
The examiner may apply another examination format when re-examining individual students.
Lab assignment 1: Resolution and logic programming Lab assignment 2: Implementation of database query systems