Introduction to Logic

Graduate Core Course in Computer Science
(August-December 2006)

Instructor Paritosh K. Pandya
Room A249
Phone: (tifr) Ext. 2551
Email:  pandya@tifr.res.in
Time:  Tuesday & Thursday: 11:30 to 13:00
 Room No. A 212
Course Page http://www.tcs.tifr.res.in/~pandya/logic06/index.html
Google Group
logictifr06@googlegroups.com

Assignments

Not Yet!!

Topics:

  • Mathematical Preliminaries: Set, Relations, Partial Orders, Well-ordered sets and principle of Noetherian induction, Structural induction, Cardinality of Sets.
  • Propositional Calculus:
        Syntax and semantics
        Hintikka's Lemma and Model Existence Theorem
        Model theory: Compactness, Lowenheim-skolem theorem, normal forms, functional completeness
        Semantic Tablaeux: soundness, completeness and decidability
        Hilbert style proof system, Sequent calculus
  • First-order logic:
        Syntax and semantics
        Hintikka's Lemma and model existence theorem
        First-order semantic Tableaux: soundness and completeness
        Hilbert style proof system for FOL, deduction theorem, Sequent calculus
        Prenex normal form, Resolution
  • First-order logic with equality:
        Canonical models, Model existence theorem
        Axiomatisation and completeness
        Upward and downward Lowenheim-Skolem Theorems
  • *** OMITTED Scope of First-order Logic:
        Axiomatisation of some mathematical structures
        ZFC set theory in FOL, Limitations of FOL
  • Decision procedures: quantifier-free formulae with uninterpreted functions with equality, theory of lists and arrays, First order real-arithmetic,  Fourier-Motzkin Variable Elimination
  • Basics of Modal and Program Logics: Kripke semantics, Correspondances, Axiomatisation: systems K, KT4, S5, completeness, decidability using filteration. Dynamic logic: axiomatisation and completeness.

  • Text Books

  • J.H. Gallier: Logic for computer science, John Wiley and Sons, 1987.
  • M. Fitting: First-order logic and automated theorem proving, Springer-Verlag, 1990.
  • H.D. Ebbinghaus, J. Flum, W. Thomas: Mathematical Logic, Springer-Verlag, 1984.
  • Assignments from last year's course

           Assignments 1 to 4 (To be submitted by November 15th)
           Assignment 5 (manoj topics)

    References and Links

        Web page of Logic course at Rice Univ.
        Decision Procedures (Manoj Raut)
        Notes on Modal Logics (R. Ramanujam)