Applied Logic
Syllabus, Master's level, 1MA058
This course has been discontinued.
- 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, 31 May 2013
- Responsible department
- Department of Mathematics
Entry requirements
120 credit points including 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 the undecidability of predicate logic (Church's theorem);
- formulate the completeness theorem of propositional and predicate logic and explain its usage;
- use and describe methods for efficient representation and solution of problems in propositional logic;
- formalise problems in modal, propositional and predicate logic;
- explain different interpretations of modal operators and applications to model checking problems;
- reason model-theoretically in predicate and modal logic;
- give an account for some calculus and system for automatic proof search in predicate logic;
- give an account for some decision method for equational logic;
- use a proof support system based on a logical framework;
- explain the algorithmic interpretation of intuitionistic logic and the principles of program extraction from proofs.
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 examination at the end of the course combined with assignments given during the course.