Date: 2013-11-13
Categories: news; teaching

PhD student course on logic, proof and mechanized theorem proving

On Wed 2013-11-13 and Wed 2013-11-20 I am giving a course on logic, proof and theorem proving to current PhD students. The following is my rough plan for the two sessions (each 1 hour long). Students are expected to read material beforehand.

Reading:

  * basic background

    http://www.paultaylor.eu/stable/prot.pdf
    Ch.s 1-5 (4 is slightly less important for theorem proving)

    http://en.wikipedia.org/wiki/Logical_connective

    http://en.wikipedia.org/wiki/Natural_deduction

    http://en.wikipedia.org/wiki/Sequent_calculus


  * intro to proof theory:

    http://plato.stanford.edu/entries/proof-theory-development/


  * the system LJ:

    http://www.normalesup.org/~saurin/Enseignement/Proof_Theory_CMI/cours3.pdf

Session 1:

1st session
===========

  Connectives

  Propositional logic

  Meaning of propositional statements, truth tables

  Propositional proofs 

    Two types of proof: ND, sequent calculus

  Quantifiers

  Meaning of statements involving quantifiers, models

  First-order proofs (ND, sequent calculus)

  System G3i

  The cut rule

  Proof and types

Session 2:

2nd session
===========

  Introduction to HOL

  Basic steps with HOL

  Simple proofs

  First-order automated proof

  Simplification  

  Induction