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

Code	Subject	
MML1015	Temporal Logic	

Section	Semester	Hours: C+S+L	Category	Type	
Formals Methods in Programming - in English	2	2+2+0	speciality	compulsory	

Teaching Staff in Charge	Assoc.Prof. BREAZ Simion Sorin, Ph.D., bodo@math.ubbcluj.ro	
Aims	We will present basic facts on Temporal Logic and applications in formal programming. By the graduation of this class, the students will get the following competences:
 - Understanding the syntax and semantics in Temporal Logic
 - Using temporal properties
 - Realizing algorithmic verifications that a given logic formula holds in a given structure
 - Using formal execution sequences and Temporal Logic&#8217;s  objects in Programming
	
Content	 1.Concepts and notions in Classical Logic.
 2.Propositional Temporal Logic. Language and semantics.
 3.Propositional Temporal Logic. Laws and Operators.
 4.Axiomatization of Propositional Temporal Logic.
 5.First order Temporal Logic.
 6.Programs. Execution Sequences.
 7.Program Axioms and Program Properties.
 8.Basic Invariant Method. Applications.
 9.Invariant Methods for Precedente Properties. Applications.
10. Fair Execution Sequences. The Finite Chain Reasoning Method.
11.Well-Founded Orderings.
12.Special Methods for Sequential Programs.
	
Bibliography	1.Chomicki, J., Toman, D.: Temporal Logic in Information Systems, BRICS Lecture Series, 1997.

2.Kroger, F.: Temporal Logic and Programs, Springer-Verlag, 1987.

3. Breaz, S., Covaci, R.: Elemente de logica matematica, teoria multimilor si aritmetica, editura EFES, 2006.

Assessment	A written final exam (grade E), a test at the seminar (grade T) and a referee (R). The exam subjects have theoretical questions from all the studied topics, and one problem, among the problems studied at the course and last 4 seminars. The test subject have
practical questions (exercices and problems) from topics which are studied in first 10 weeks. The final grade is the weighted mean of the three grades mentioned above, conditioned by all the grades being at least 5 from 10. Otherwise, the exam will not be passed.
The final grade = 50%E + 25%T + 25%R.