Babes-Bolyai University of Cluj-Napoca
Faculty of Mathematics and Computer Science
Study Cycle: Graduate

SUBJECT

Code
Subject
MII0006 Automated Theorem Proving Systems
Section
Semester
Hours: C+S+L
Category
Type
Computer Science - in English
4
2+0+2
speciality
optional
Information engineering - in English
6
2+0+2
optional
Information engineering - in English
8
2+0+2
optional
Teaching Staff in Charge
Lect. LUPEA Mihaiela, Ph.D.,  lupeacs.ubbcluj.ro
Aims
- To study proof methods, which solve specific decisional problems in propositional
logic and first-order logic: check if a statement is a theorem or if a statement (the
conjecture) is a logical consequence of a set of statements (the axioms and hypotheses)
- To implement ATP (automated theorem prover) systems based on the studied methods.
Content
1. Automated theorem proving systems: architecture, examples, applications.
2. Basic notions of classical logics (propositional logic and first-order logic).
3. Data structures used to represent and manipulate logical formulas.
4. Binary decision diagrams in propositional logic.
5. Semantic tableaux method - a refutation proof method
- A new approach of semantic tableaux method;
- Considerations for implementation of an ATP based on this method.
6. Sequent and anti-sequent calculi- two complementary direct proof systems
- Sequent calculus - used to check the derivability in propositional/first-order
logic.
- Anti-sequent calculus- used to check the non-derivability and to build anti-models.
- Considerations for implementation of an ATP based on these methods.
7. Semantic trees
- Heuristics and tree-searching methods used to implement an efficient proof
procedure based on the construction of semantic trees.
8. Model elimination calculus - a refutation proof method
- Connection tableaux used to find a refutation in clausal form
9. Resolution method - a refutation proof method
Refinements of resolution
- lock resolution
- linear resolution (input, unit, ordered);
- semantic resolution (hyper-resolution, the set-of support-strategy, ordered)
Considerations for implementation of ATP systems based on different refinements of
resolution.

Laboratory:
1. Study and work with some dedicated ATP systems.
2. Projects for teams of 3 students: implementation of ATP systems based on the studied
methods.
References
1. M. Ben-Ari: Mathematical Logic for Computer Science, Ed. Springer, 2001.
2. C.L.Chang, R.C.T.Lee: Symbolic Logic and Mechanical Theorem Proving, Academic Press,
1973.
3. M.Fitting: First-order Logic and Automated Theorem Proving, Texts and Monographs in
Computer Science, Springer Verlag, 1990, Second Edition 1996.
4. M.R. Genesereth, N.J. Nilsson: Logical Foundations of Artificial Intelligence, Morgan
Kaufman, 1992.
5. D.A. Duffy: Principles of automated theorem proving, John Willey & Sons, 1991.
6. L.C. Paulson: Logic and Proof, Univ. Cambridge, 2000, course on-line.
7. M. Possega: Deduction Systems, Institute of Informatics, 2002, course on-line.
8. S.Reeves, M.Clarke: Logic for computer science, Addison Wesley Publisher Ltd, 1990.
9. D.Tatar: Inteligenta artificiala: demonstrarea automata si NLP, Editura
Microinformatica, Cluj-Napoca, 2001.
10. R.M.Smullyan: First-order logic, Revised Edition, Dover Press, New York, 1996.

Assessment
The final grade is obtained based on:
- written exam: 50%
- laboratory activity: 50%
Links: Syllabus for all subjects
Romanian version for this subject
Rtf format for this subject