Applied Logic

10 credits

Syllabus, Master's level, 1MA058

This course has been discontinued.

A revised version of the syllabus is available.

Code: 1MA058
Education cycle: Second cycle
Main field(s) of study and in-depth level: Computer Science A1N, Mathematics A1N
Grading system: Fail (U), Pass (3), Pass with credit (4), Pass with distinction (5)
Finalised by: The Faculty Board of Science and Technology, 15 March 2007
Responsible department: Department of Mathematics

Entry requirements

BSc, Logic and Proof Techniques I, Automata Theory

Learning outcomes

In order to pass the course (grade 3) the student should be able to

give an account of important concepts and definitions in the area of the course;

exemplify and interpret important concepts in specific cases;

formulate important results and theorems covered by the course;

describe the main features of the proofs of important theorems;

express problems from relevant areas of applications in a mathematical form suitable for further analysis;

use the theory, methods and techniques of the course to solve mathematical problems;

present mathematical arguments to others.

Higher grades, 4 or 5, require a higher level of proficiency. The student should be able to solve problems of greater complexity, i.e. problems requiring a combination of ideas and methods for their solution, and be able to give a more detailed account of the proofs of important theorems and by examples and counter-examples be able to motivate the scope of various results. Requirements concerning the student's ability to present mathematical arguments and reasoning are greater.

Content

Propositional logic: combinatorial problems as propositional problems. Methods for efficient solution and representation of propositional problems (Davis–Putnam, BDDs).

Modal logic: possible worlds semantics, Kripke models.

Interpretations of modal logic: Temporal logic and epistemic logic. Applications in model checking.

Equational logic: terms, unification, universal algebra, equational reasoning, term rewriting.

Predicate logic and proof search: the completeness theorem, proof search in some calculi (tableaux, resolution).

Solvable and unsolvable problems: complete and decidable theories, quantifier elimination, Gödel's incompleteness theorem (without proof).

Constructive logic and type theory: lambda calculus, simple type theory, intuitionistic logic, Martin-Löf type theory, propositions-as-types, program extraction from proofs, logical frameworks, proof support systems (Coq, Hol, Isabelle or Agda).

Instruction

Lectures and problem solving sessions.

Assessment

Written and, possibly, oral examination at the end of the course. Moreover, compulsory assignments may be given during the course.