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The Australian National University

Program outline

Week 1

Fundamentals of Metalogic
John Slaney
  • Metatheory of classical first-order logic, including completeness theorem
  • Basics of proof theory
  • The Joy of Sets
Computability and Incompleteness
Michael Norrish
  • Computability, recursiveness, Turing machines
  • Diagonalisation
  • Peano Arithmetic and Gödel numbering
  • Undecidability of first-order logic
  • Incompleteness of Peano Arithmetic
Introduction to Modal and Temporal Logic
Rajeev Gore
  • Kripke models, Hilbert calculi, Frame correspondences
  • Tableaux-based decisions procedures
  • Propositional linear temporal logic
Introduction to Proof Theory
Anupam Das
  • Propositional logic, semantics and proofs.
  • Soundness and completeness.
  • First-order logic and some formal theories.
  • The sequent calculus and cut-elimination.
  • Perspectives.

Week 2

Overview of Automated Reasoning
Peter Baumgartner
  • Automated propositional theorem proving
  • Automated first-order theorem proving
  • Reasoning with arithmetic constraints by quantifier elimination
Deviant Logic
John Slaney
  • Philosophical motivation
  • Routley-Meyer semantics
  • Paraconsistency and the γ rule
  • Deviant theories of arithmetic
Constructive Logic and Realisability
Dirk Pattinson
  • Constructive Reasoning by Example
  • BHK interpretation
  • Natural Deduction for FOL
  • Goedel Gentzen
  • Heyting Arithmetic
  • Realisability Interpretation
  • Disjunction Theorem
  • Heyting Arithmetic in Higher Types
  • Modified Realisability
Tableaux metatheory for propositional and syllogistic logics
Tomasz Jarmużek
  • Tomasz Jarmużek
  • TBA
  • TBA
  • TBA

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