The computer itself was born from logic, and logic plays indispensable roles in diverse fields of science today, including computer science, mathematics, linguistics, philosophy and beyond. This course covers advanced issues in classical logic and elements of non-classical logic with emphasis on completeness proof methodologies for various logical systems; (in)completeness is the most fundamental issue in logic, elucidating the relationships between the syntax (proof theory) and semantics (model theory) of logical systems, or the correspondence between symbolic language and reality/worlds. Familiarity with elementary logic is assumed as well as general mathematical knowledge (such as sets, relations, quotients under equivalence relations).
Learning Outcomes
Upon successful completion, students will have the knowledge and skills to:
- Understand classical and non-classical logical systems and their significance
- Evaluate differences (advantages/disadvantages) of logical systems
- Analyse the syntax and semantics of logics and their meta-theoretical properties
- Apply translation principles for comparing different logical systems
- Create mathematical proofs in the area of formal logic
- Reflect on common logical systems and evaluate their limitations
Indicative Assessment
- Assignment (50) [LO 1,2,3,4,5,6]
- Exam (50) [LO 1,2,3,4,5,6]
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Workload
Approximately 130 hours of study consisting of 24 hours lectures and 22 hours tutorials (i.e., two one-hour lectures every week and one two-hours tutorial every week except for the first week) and self-directed study.
Inherent Requirements
Information on inherent requirements for this course is currently not available.
Requisite and Incompatibility
Prescribed Texts
The Open Logic Text by the Open Logic Project, available at: https://builds.openlogicproject.org/open-logic-complete.pdf
Preliminary Reading
Jeremy Avigad, Logic and Computation, CMU (Carnegie Mellon University) Lecture Notes, 2002, available at: https://www.andrew.cmu.edu/user/avigad/Teaching/landc_notes.pdf
Dirk van Dalen, Logic and Structure, Springer, 2013
Johan van Benthem, Modal Logic for Open Minds, CSLI Publications, 2010
Patrick Blackburn, Maarten de Rijke and Yde Venema, Modal Logic, Cambridge University Press, 2001
Nick Bezhanishvili and Dick de Jongh, Intuitionistic Logic, Lecture Notes, University of Amsterdam, 2012, available at: https://www.math.uni-hamburg.de/en/personen/khomskii/intuitionistic/PP-2006-25.text.pdf
Jean-Yves Girard, Proofs and Types, Cambridge University Press, 1989
Samuel Mimram, Program = Proof, 2020, available at: https://www.lix.polytechnique.fr/Labo/Samuel.Mimram/teaching/INF551/course.pdf
Fees
Tuition fees are for the academic year indicated at the top of the page.
Commonwealth Support (CSP) Students
If you have been offered a Commonwealth supported place, your fees are set by the Australian Government for each course. At ANU 1 EFTSL is 48 units (normally 8 x 6-unit courses). More information about your student contribution amount for each course at Fees.
- Student Contribution Band:
- 2
- Unit value:
- 6 units
If you are a domestic graduate coursework student with a Domestic Tuition Fee (DTF) place or international student you will be required to pay course tuition fees (see below). Course tuition fees are indexed annually. Further information for domestic and international students about tuition and other fees can be found at Fees.
Where there is a unit range displayed for this course, not all unit options below may be available.
| Units | EFTSL |
|---|---|
| 6.00 | 0.12500 |
Course fees
- Domestic fee paying students
| Year | Fee |
|---|---|
| 2024 | $4980 |
- International fee paying students
| Year | Fee |
|---|---|
| 2024 | $6360 |
Offerings, Dates and Class Summary Links
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