I will give a lecture course in English,

Non-classical logics

starting October 5, 2000 (University Main Building, Sali 4, Thursdays 10--12). Prerequisite for the course is an introductory course in logic.

Sara Negri, logiikan dosentti

e-mail: negri@helsinki.fi
Course material can be found in the library of the Philosophy Department. Here is a list of useful references:

  • van Dalen, Logic and Structure (background, natural deduction, intuitionistic logic)
  • Troelstra and van Dalen, Constructivism in mathematics, vol. I, ch. 1,2. (Intuitionistic logic, Kripke semantics, double negation translation)
  • Negri and von Plato, Structural Proof Theory (constructive resoning, natural deduction, sequent calculus, automated deduction).
  • Fitting and Mendelsohn, First order modal logic (introduction to modal logic, possible worlds semantics)
  • Troelstra and Schwichtenberg, Basic Proof Theory, 2nd. ed. (modal embedding, linear logic)
  • Boolos and Jeffrey, Computability and Logic (provability logic, Goedel incompleteness)
  • Nagel and Newman, Gödel's proof
  • Sokal and Bricmont, Intellectual Impostures (postmodernists' abuse of Goedel incompleteness)
  • Mints, A short introduction to modal logic (tableaux calculi for modal logics)
  • Troelstra, Lectures on linear logic (linear logic).

    • There will be a final exam on December 7 (written questions on the topics treated during the course). Alternatively, a short essay on a suitable topic can be presented.

    Course calendar:

  • 5.10: Plan of the course. Introduction to non-classical logics. Review of natural deduction.
  • 12.10: Intuitionistic logic. Goedel-Gentzen double negation translation. Introduction to Kripke semantics.
  • 19.10: Kripke semantics: examples, soundness, completeness.
  • 26.10: Intermediate logics. Goedel's proof of the fact that intuitionistic logic is not finitely valued. Dummett logic.
  • 2.11: Modal logic: Introduction through possible worlds semantics. Properties of accessibility relation in modal frames and the corresponding modal axioms.
  • 9.11: Embedding of intuitionistic logic into S4. Provability logic.
  • 16.11: Formalization of Goedel incompleteness in modal logic.
  • 23.11: Substructural logics. Linear logic.
  • 30.11: Syntax and semantics of linear logic. Embedding of intuitionistic logic into linear logic.
  • 7.12: Exam (same place, same time as the lectures).

    • Back to Sara's homepage.

    Last modified November 16, 2000