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School of Computing · ANU College of Engineering Computing & Cybernetics
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).
Assignment
Learning outcomes 1, 2, 3, 4, 5, 6
Exam
Learning outcomes 1, 2, 3, 4, 5, 6
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.
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