From syllogism to common sense: a tour through the logical landscape

Lecturers

Dr. Mehul Bhatt, Dr. Oliver Kutz, Dr. Thomas Schneider
 

Audience

Diplom, MSc, and PhD students in computer science, mathematics, philosophy and related subjects
 

Hours

V2Ü1 – 90min lecture, break, 45min tutorial
 

Time and place

Thu 16:00–18:00 and 18:00–19:00 MZH 1110 (exceptions: 3rd and 17th Nov in MZH 3150)

Abstract

• Syllogism
• Propositional logic
• Intuitionistic logic
• Strict implication and modal logic
• Many-valued and fuzzy logic
• Description logic
• First-order logic
• Common-sense logic: event calculus, situation calculus, default logic

We will discuss intuitions and important theoretical aspects, and will demonstrate tools where they exist. Every lecture will be accompanied by exercises, to be discussed in the following week. There is no prerequisite for taking this course.

Materials

3.11.11, Introduction and overview

Slides

PDF     PDF, 4 on 1     (only Oliver's and Thomas's part)

10.11.11, Categorical propositions and syllogisms

Slides

PDF     PDF, 4 on 1

Literature

Chapters 5, 6.1, 6.2 of
I. Copi, C. Cohen and K. McMahon: Introduction to Logic, 14th ed., Prentice Hall, 2011.
In SUUB: Magazin 02 E 2115, Zentrale/Eb. 2 h sow 032 f/416(12), a sow 032 f/416(12)a
Scans are available under "Dateien" in StudIP.

Exercises

Sheet 1 PDF, to be discussed on 17 Nov.

17.11.11, Categorical syllogisms

Slides

PDF     PDF, 4 on 1     (short summary of the 1st part from 10.11.11, plus slightly revised 2nd part)

Literature

Chapters 6.3–6.5 of
I. Copi, C. Cohen and K. McMahon: Introduction to Logic, 14th ed., Prentice Hall, 2011.
In SUUB: Magazin 02 E 2115, Zentrale/Eb. 2 h sow 032 f/416(12), a sow 032 f/416(12)a
Scans are available under "Dateien" in StudIP.

(Further reading: Appendix of Chapter 6, and Chapter 7)

Exercises

Sheet 2 PDF, to be discussed on 24 Nov.

24.11.11, Propositional logic (intro)

Slides

PDF     PDF, 4 on 1

Literature

Chapter 1 of
W. Rautenberg: A Concise Introduction to Mathematical Logic, Springer, 2010.
This edition at Universitext: DOI 10.1007/978-1-4419-1221-3\_1
German version of 2008: DOI 10.1007/978-3-8348-9530-1
Scan is available under "Dateien" in StudIP.

Exercises

Sheet 3 PDF, to be discussed on 1 Dec.

1.12.11, Propositional logic (semantic equiv., tautologies, logical consequence)

Slides

PDF     PDF, 4 on 1

Literature

as for the previous lecture

Exercises

Sheet 4 PDF, to be discussed on 8 Dec.

8.12.11, Propositional logic (Natural deduction, Hilbert calculi)

Slides

PDF     PDF, 4 on 1

Literature

as for the previous lecture

Exercises

Sheet 5 PDF, to be discussed on 15 Dec.

15.12.11, Intuitionistic logic

Slides

PDF     PDF, 4 on 1

Literature

• A. Chagrov, M. Zakharyaschev: Modal Logic. Oxford Logic Guides, Volume 35, 1997.
  Unfortunately unavailable in SUB. (Ask us if you want to consult the book.)
• M. Fitting: Proof Methods for Modal and Intuitionistic Logic. Reidel, 1983.
  Unfortunately unavailable in SUB. (Ask us if you want to consult the book.)
• T. Mossakowski, A. Tarlecki, R. Diaconescu: What is a logic translation? Logica Universalis, 3(1), pp. 95–124, 2009.
  Available online in SUB.

Exercises

Sheet 6 PDF, to be discussed on 22 Dec.

22.12.11 cancelled

12.1.12, Conditionals

Slides

PDF     PDF, 4 on 1     with errors corrected on Slides 27, 28

Literature

• G. Priest: An Introduction to Non-Classical Logic, 2nd ed., Cambridge, 2011. (Sections 1.6–1.10, 4.5–4.7, 6.6, 9.7)
  Not available at SUB; ask us if you want to read it.
• F. Jackson: Conditionals, Oxford, 1991. (Introduction for overview; individual essays for deeper insights)
  Available at SUB.

Exercises

Sheet 7 PDF, to be discussed on 19 Jan.     with errors corrected

19.1.12, Modal logic

Slides

PDF     PDF, 4 on 1     We only covered Slides 1–23 in the lecture; see also Slides 41, 42 for summary and literature.

Literature

See last slide.

Exercises

Sheet 8 PDF, to be discussed on 26 Jan.

26.1.12, Quantification

Slides

PDF     PDF, 4 on 1

Literature

See last slide.

Exercises

Sheet 9 PDF, to be discussed on 2 Feb.