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Computer-Supported Modeling and Reasoning - Lectures

Date Topic
25.10.2006 Organizational matters, Introduction, Propositional logic
03.11.2006 First-order logic
08.11.2006 Equality
15.11.2006 Theories, Sets, The lambda-calculus
22.11.2006 The lambda-calculus
29.11.2006 Metatheory: Representing syntax in the typed lambda-calculus, Resolution, Proof Search
06.12.2006 Rewriting, Isabelle's Metalogic
13.12.2006 Isabelle's Metalogic
15.12.2006 Isabelle's Metalogic, HOL: Introduction
18.12.2006, 14:15-16:00, Room 051-00-034 Some Isabelle and HOL Applications, Presentation on XML
10.01.2007 HOL: Derived Rules, Conservative extensions
12.01.2007 Conservative extensions, HOL Library, Orders
17.01.2007 Sets, Functions, Background: Recursion, Induction, and Fixpoints, Least Fixpoints
24.01.2007 Well-Founded Recursion
26.01.2007 Arithmetic
31.01.2007 Datatypes, Imperative Languages
07.02.2007 Imperative Languages
14.02.2007 Imperative Languages

Lecture Notes for printout (work in progress)

Screen Notes for online study

The course is now finished.


Books and articles

  • D. van Dalen: Logic and Structure. Springer-Verlag, 1980. An introductory textbook on logic
  • Michael Huth and Mark Ryan: Logic in Computer Science. Modelling and Reasoning about Systems. Cambridge University Press, 2004. This book covers many of the topics of the lecture. It is interesting because it uses a style of doing natural deduction proofs that is different from the one we use in the lecture.
  • Simon Thompson: Type Theory and Functional Programming. Addison-Wesley, 1991. Chapter 1 is an introduction to propositional and first-order logic. Chapter 2 is an introduction to the lambda-calculus.
  • David Basin and Seán Matthews: Logical Frameworks. In Dov Gabbay and Franz Guenthner, editors, Handbook of Philosophical Logic, second edition. Reidel, 2002.
  • N.G. de Bruijn: A Survey of the Project AUTOMATH. In Essays in Combinatory Logic, Lambda Calculus, and Formalism. Academic Press, 1980.
  • Robert Harper, Furio Honsell, and Gordon D. Plotkin: A Framework for Defining Logics. Journal of the ACM, 40(1):143-184, 1993.
  • Arnon Avron, Furio Honsell, Ian A. Mason, and Robert Pollack: Using Typed Lambda Calculus to Implement Formal Systems on a Machine. Journal of Automated Reasoning 9(3):309-354, 1992
  • Henk Barendregt: Introduction to Generalized Type Systems. Journal of Functional Programming 1(2):125-154, 1991.
  • Lawrence C. Paulson: Isabelle: A Generic Theorem Prover. Springer LNCS 828, 1994.
  • Tobias Nipkow: Hoare Logics in Isabelle/HOL. In H. Schwichtenberg and R. Steinbrüggen, editors, Proceedings of Proof and System-Reliability, pages 341-367, Kluwer, 2002.

Manuals and Tutorials


Related Lectures

  • Larry Paulson: Logic and Proof. An introductory lecture on logic, mainly on syntax and semantics of propositional and first-order logic, and proof systems for those logics.
  • Frank Pfenning: Automated Theorem Proving.