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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
Finite model theory
Qing Wang
  • Finite model theory
  • Inexpressibility proofs
  • Descriptive complexity
Computability and Incompleteness
Michael Norrish
  • Computability, recursiveness, Turing machines
  • Diagonalisation
  • Peano Arithmetic and Goedel 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
Overview of Automated Reasoning
Peter Baumgartner
  • Automated propositional theorem proving
  • Automated first-order theorem proving
  • Reasoning with arithmetic constraints by quantifier elimination

Week 2

An introduction to Proof Theory
Agata Ciabattoni and Shawn Standefer
  • Basic sequent calculus; cut elimination
  • Sequent calculi for substructural logics
  • Hypersequents and yet more logics
Axiomatic Object Theory
Ed Zalta
  • Axioms and logical objects
  • Situations, possible and impossible worlds
  • Concepts, counterparts and compossibility
  • Forms, fictions and Fregean senses
  • Mathematical objects

1 - 2 more courses TBA

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