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Module MA2361: Computation Theory and Logic

Credit weighting (ECTS)
5 credits
Semester/term taught
Michaelmas term 2018-19
Contact Hours

11 weeks, including tutorials which will be held in lecture slots, and a review period at the end of term.

Prof. Colm Ó Dúnlaing
Learning Outcomes
On successful completion of this module students will be able to
  • Construct very simple Turing machine programs.
  • Construct proofs of formulae in propositional and first-order logic, including resolution, the Deduction Theorem, and derived rules.
  • Determine the solvability or otherwise of various computational problems.
  • Extend their knowledge of mathematical logic or proceed to further study of the subject.
Module Content
  • Turing machines, universal Turing machine, halting problem, recursion (fixpoint) theorem, recursive separability, (total) recursive functions are not even semidecidable.
  • Propositional logic, resolution, Frege's axioms I--III, deduction theorem, completeness.
  • First-order theories, axioms IV, V models, skolem forms, Herband's Theorem, completeness of first-order logic.
  • Peano Arithmetic, representability of arithmetic functions, Gödel's first incompleteness theorem, Tarksi, and Church, as regards computability. Gödel's Theorem, original version.
  • Consistency: Hilbert-Bernays derivability conditions I--III, deduction of Goedel's second incompleteness theorem. Another view: consistency related to recursiveness.
Module Prerequisite
None beyond SF level modules.
Assessment Detail

2-hour examination in December 2018, counting for 80%.  Fortnightly quizzes will count for 20%. .