7AAN2015 First-Order Logic
THIS MODULE IS NOT RUNNING IN 2017-18
Credit value: 20
Module tutor: Dr Nils Kürbis
- Formative assessment: regular logic exercises
- Summative assessment: one two-hour exam (100%) in May/June
Students are reassessed in the failed elements of assessment and by the same methods as the first attempt.
Teaching pattern: One two-hour weekly lecture and one one-hour weekly seminar over ten weeks.
Sample syllabus: 7AAN2015 module syllabus 2016-17
- This module will be taking more of a formal, technical approach to its material than a philosophical one: it is important that students should have some competence in elementary symbolic logic (or at least mathematics)
- The module is designed as a foundation for 7AAN2043 Mathematical Logic: Limitative Results. Although the two modules are formally independent, and there is no obligation on students to proceed on from one to the other, that would be the natural expectation.
- The lectures will be shared with students taking 6AANA028 First-Order Logic throughout both hours, although in other respects those students may be subject to different requirements.
This module, together with 7AAN2043 Mathematical Logic, alternates annually with comparably formal modules in Modal Logic and Set Theory.
Students will be acquainted with the basic metatheory of propositional and first- order quantifier logic. This includes proofs of (1) soundness: the given deducibility systems permit us to deduce only what is logically valid, (2) completeness: the systems permit deduction of all of what is logically valid, and (3) compactness. On the way, students should acquire some familiarity with basic reasoning techniques and basic semantic concepts, such as interpretation, satisfaction, truth under an interpretation, model, concepts relevant to topics in philosopical logic, e.g. validity, consequence.
After successfully completing the course the students will be able to demonstrate intellectual, transferable and practicable skills appropriate to a Level 6 module and in particular will be able to demonstrate:
- understanding of the semantics and axiomatics of propositional and first-order logic
- understanding of logical derivations
- understanding of mathematical structures as represented in logic
- understanding of the proof of compactness
- understanding of the proof of completeness
Course book: Enderton, H. A Mathematical Introduction to Logic 2nd edition. San Diego, Cal: Academic Press 2001.
Recommended additional texts:
- W. Hodges, ``Logic''. Penguin books, Middx, 1977.
- J. Barwise, J. Etchemendy, `` The Language of First-order logic'' CSLI, 1991.
- Boolos, G. & Jeffrey, R. Computability and Logic. 3rd edition. Cambridge: Cambridge University Press 1989.
Its special characteristic is that it presents proof that various accounts of computability coincide. Another famous textbook that covers the much the same ground is:
- Mendelson, E. Introduction to Mathematical Logic. 4th ed. London: Chapman & Hall 1997.
A fine textbook for graduate level students, with material that is not found in other textbooks is:
- Shoenfield, J. Mathematical Logic. Reading, Mass.: Addison-Wesley 1967.
- Bell, J. & Machover, M. A Course in Mathematical Logic. Amsterdam: North-Holland 1977
The modules run in each academic year are subject to change in line with staff availability and student demand so there is no guarantee every module will run. Module descriptions and information may vary depending between years.