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

Code	Subject	
MII0020	Automated Theorem Proving	

Section	Sem.	Hours: C+S+L	Category	Type	
Computer Science - in English	4	2+0+1	speciality	optional	
Information engineering - in English	4	2+0+1	complementary	optional	

Teaching Staff in Charge	Lect. LUPEA Mihaiela, Ph.D., lupea@cs.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.
	
Bibliography	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. D.A. Duffy: Principles of automated theorem proving, John Willey & Sons, 1991.
4. M.Fitting: First-order Logic and Automated Theorem Proving, Texts and Monographs in 
   Computer Science, Springer Verlag, 1990, Second Edition 1996.
5. M.R. Genesereth, N.J. Nilsson: Logical Foundations of Artificial Intelligence, Morgan 
   Kaufman, 1992.
6. M.Lupea, A.Mihis: Logici clasice si circuite logice. Teorie si exemple, Ed.Albastra, 
   editia 2, 2009.
7. L.C. Paulson: Logic and Proof, Univ. Cambridge, 2000, course on-line.
8. M. Possega: Deduction Systems, Institute of Informatics, 2002, course on-line.
9. R.M.Smullyan: First-order logic, Revised Edition, Dover Press, New York, 1996.
10. D.Tatar: Inteligenta artificiala: demonstrarea automata si NLP, Editura 
   Microinformatica, Cluj-Napoca, 2001.

Assessment	The final grade is obtained based on:
- written exam: 50%
- laboratory activity: 50%