Predicate and Propositional Logic > Propositional and Predicate Logic

Propositional and Predicate Logic

Published on Sept. 28, 2016, 9:37 p.m.

Lecture

The topics from the lecture will be covered in the lecture notes (GitHub repository, pdf). These were written last year and some small changes may happen this year. If you find any errors in the lecture notes, or if you believe some parts could be explained better, let me know.

You may also be interested in the presentations and other information from last year on Petr Gregor's web.

Past Lectures

This is the log of past lectures. "LN" refers to the lecture notes mentioned above.

Date Topic
October 4, 2018 Introduction, propositional logic - formulas (LN pages 1-13)
October 11, 2018 Propositional logic - formulas, models, normal forms (LN pages 13-17)
October 18, 2018 Propositional logic - normal forms, theories, SAT solvers (glucose) (LN pages 17-18)
October 25, 2018 Propositional logic - theories, analysis of finite theories, 2-SAT (LN pages 18-21)
November 1, 2018 Propositional logic - tableau method, soundness, completeness (LN pages 23-29)
November 8, 2018 Compactness. Resolution method - soundness and completeness, linear resolution (LN pages 29-35)
November 15, 2018 Completeness of LI resolution for Horn formulas, introduction to predicate logic - basic syntax (LN pages 35-44)
November 22, 2018 Open Day - lecture cancelled

Exam

The exam consists of an exam test and an oral exam. A prerequisite for the exam is the credit from the seminar. Details will be added later.

Additional reading

  1. A. Nerode, R. A. Shore, Logic for Applications, Springer, 2nd edition, 1997.
  2. P. Pudlák, Logical Foundations of Mathematics and Computational Complexity - A Gentle 3. Introduction, Springer, 2013.
  3. J. R. Shoenfield, Mathematical Logic, A. K. Peters, 2001.
  4. W. Hodges, Shorter Model Theory, Cambridge University Press, 1997.
  5. W. Rautenberg, A concise introduction to mathematical logic, Springer, 2009.

Seminar

Credit requirements

There will be two tests during the term (one on propositional and one on predicate logic). It will be possible to get 10 points for each test. There will also be 3 homework assignments, each for 2 points. In order to obtain the credit for the seminar (which is required before you can take the exam), you need to obtain at least 16 points.

Homeworks

  1. k-colorable graphs and SAT - deadline October 31, in the evening, see linked zip for details.

  2. propositional logic - deadline is November 13, in the evening, see the linked pdf for questions

Exercises from the seminar

We will mostly use the exercises from Petr Gregor's seminar.

Date Topic
October 4, 2018 Introduction, syntax vs. semantics, propositional formulas vs first-order and higher-order formulas (PG seminar 1, exercise 1-2)
October 11, 2018 Formulas with a given meaning in propositional, and first-order languages, adequacy of sets of connectives, CNF and DNF using models (PG seminar 1, ex. 3, 5, 6, and seminar 2, ex. 5, 6)
October 18, 2018 Adequacy, CNF and DNF, HornSAT (PG seminar 2)
October 25, 2018 Implication graph (PG seminar 3, ex. 3, 5, and 9)
November 1, 2018 Tableau method in propositional logic (PG seminar 4, ex. 3-5)
November 8, 2018 Compactness. Resolution (PG seminar 5, ex. 4, 5, 6a, 8)
November 15, 2018 LI-resolution, Hilbert calculus, basics of syntax in predicate logic. (PG seminar 6, ex. 1, 4-6)
November 22, 2018 Open Day - seminar cancelled