Logic and Proof Techniques I
Syllabus, Bachelor's level, 1MA027
- Code
- 1MA027
- Education cycle
- First cycle
- Main field(s) of study and in-depth level
- Mathematics G1F
- Grading system
- Fail (U), Pass (3), Pass with credit (4), Pass with distinction (5)
- Finalised by
- The Faculty Board of Science and Technology, 25 April 2012
- Responsible department
- Department of Mathematics
Entry requirements
Algebra I.
Learning outcomes
In order to pass the course (grade 3) the student should be able to
- explain how the formulas in predicate logic can be interpreted as true or false;
- translate statements and reasoning from natural language to propositional and predicate logical language;
- explain the concepts tautology, valid syllogism, logical truth and logical consequence;
- convert propositional logic formulas to disjunctive and conjunctive normal form;
- determine, in elementary cases, if a propositional or predicate logical argument is valid and, in that case, implement a formal proof of the deduction or otherwise give a counterexample to the argument;
- formulate the soundness theorem and the completeness theorem, explain their meaning and apply them in concrete examples.
Content
Language of propositional logic and languages of predicate logic. Functionally complete set of connectives. Formalisation of natural language. Induction over terms and formulas. Tautology, evaluation, counter example evaluation. Truth table. Disjunctive and conjunctive normal form. Structure for a given first order predicate language. Interpretation of a first order language in a structure. Model and counter model. Satisfiability. Axioms for a theory. Provability, natural deduction, consistency and independence. The concepts of soundness and completeness of a proof system. Incompleteness. Boolean algebra. Briefly about the difference between classical and intuitionistic logic.
Instruction
Lectures, lessons and assignments.
Assessment
Written (4 credits) and oral examination (1 credit).
Reading list
- Reading list valid from Autumn 2023
- Reading list valid from Autumn 2022
- Reading list valid from Spring 2022
- Reading list valid from Autumn 2019
- Reading list valid from Autumn 2017
- Reading list valid from Autumn 2012, version 2
- Reading list valid from Autumn 2012, version 1
- Reading list valid from Autumn 2010, version 2
- Reading list valid from Autumn 2010, version 1
- Reading list valid from Autumn 2007, version 2
- Reading list valid from Autumn 2007, version 1