Topics in Automated Theorem Proving (236 714): SS 2015
Homepage:
http://cs.technion.ac.il/~janos/COURSES/THPR2015/index.html
Old Homepage 2013/14:
http://cs.technion.ac.il/~janos/COURSES/THPR/index.html
Lecturer: Prof. J.A. Makowsky
Taub 628, Tel: 4358, email: janos@cs
Format: 2 hours lecture + 1 hour tirgul
Note the change!
Lecture: Wedneday 14:3016:30 (Starting March 18)
Tirgul: Wednesday 16:3017:30 (starting March 18)
Place: Taub 401
Last given:
By J.A. Makowsky (2013/14, 2006/7, 2003, 1989/90), by Monty Newborn (1992/93)
Prerequisites:
Logic for CS (234 292) or Set Theory and Logic (234 293)
Slides for 2015
Projects

The Area Method by Chou, Gao and Zhang.
Paper by Janicic, Narboux and Quaresma.
Students: Sharon Ron and Adi Sosnovich

Geometry in PROLOG. Paper by Coelho and Pereira.

Highschool Geometry. Paper by Singhal, Henz and McGee.
Course outline:
Automated theorem proving is used in two rather different ways.
Universal formalisms are used in Artificial Intelligence
and Databases to automatize deductive systems in general data and
knowledge processing. The Highly specialized formalisms are used
in well structured applications such as computational geometry
and other branches of computer aided mathematics.
We shall study both approaches in a certain depth.

Theorem proving and computer aided mathematics.
General problem solvers vs Special problem solvers.
Guiding problem: Classical geometry.

Propositional theorem proving: Solving SAT
Resolution methods:
Analysis of worst case, average case, heuristics.
Other methods

First Order Logic and Theorem proving.
Resolution and Unification.

Equational logic.

Classical geometry.
Course goal:
Exploring the achievements of automated theorem proving.
Introducing topics for
M.Sc. and Ph.D. theses.
Course requirements:
Four homework assignements.
Projects or take home exam.
Literature:
No single textbook covers our approach.
The most updated reference is:

J. Harrison, Handbook of Practical Logic and Automated Reasoning, Cambridge University Press, 2009

A. Robinson and A. Voronkov, eds
Handbook of Automated Reasoning, vol. 1 and 2
The MIT Press and North Holland, 2001
Additional references:

Recent papers of interest, to be posted when relevant.

ShangChing Chou, Mechanical Geometry Theorem Proving,
Reidel, 1988

WenTsuen Wu, Mechanical Theorem proving in Geometries, Springer 1994

B.F. Caviness and J.R. Johnson (eds),
Quantifier Elimination and Cylindrical Algebraic Decomposition,
Springer 1998