## "Babes-Bolyai" University of Cluj-Napoca Faculty of Mathematics and Computer Science

 Mathematical foundations of Computer Science
 Code Semes-ter Hours: C+S+L Credits Type Section MIF0001 1 2+2+0 6 compulsory Informatică
 Teaching Staff in Charge
 Prof. TATAR Doina, Ph.D., dtatar cs.ubbcluj.ro
 Lect. ROBU Judit, Ph.D., robu cs.ubbcluj.ro
 Lect. LUPEA Mihaiela, Ph.D., lupea cs.ubbcluj.ro
 Asist. MIHIS Andreea Diana, mihis cs.ubbcluj.ro
 Aims The aims of the course is the presentation of logic foundations for computer science: propositional and predicate calculus, boolean algebra and boolean functions. The connection with logic programming and logical circuits is presented. Additionally, the codes of information representation are introduced.
 Content 1. The propositional and predicate calculus, from algebraic point of view and as deductive systems. Normal forms. Decidability problem in predicate calculus: direct and by refutation methods of theorem proving (Herbrand method, resolution method). 2. Boolean algebra, boolean functions and applications. Canonic and maximal monoms. Simplification of boolean functions by Veitch, Mc. Quine and Moisil methods. Boolean equations. 3. Combinational and sequential circuits. 4. Systems of numeration, conversions. The direct, inverse, and complementary codes. Theorems of addition. Representation of numeric information.
 References 1. Cl.BENZAKEN: Systeme formels. Introduction a la logique, ed.Masson, 1991. 2. M.CLARKE: Logic for Computer Science, ed. Addison-Wesley 1990. 3. J.P.DELAHAYE: Outils logiques pour l'intelligence artificielle, ed.Eyrolls, 1986. 4. M.FITTING: First-order logic and Automated Theorem Proving, Ed.Springer Verlag, 1990. 5. L.C. PAULSON : Logic and Proof, U. Cambridge, 2000, curs on-line. 6. D.TATAR: Inteligenta artificiala: demonstrare automata de teoreme si NLP, Ed. Microinformatica, 2001. 7. D.TATAR: Bazele matematice ale calculatoarelor, litografiat, editia 1993, editia 1999. 8.(ed) A.THAYSE: From standard logic to Logic Programming, ed.J.Wiley, vol1(1989), vol2(1989), vol3(1990). 9. M. BEN-ARI: Mathematical Logic for Computer Science, Ed. Springer, 2001. 10. M. POSEGGA: Deduction Systems, Inst. of Informatics, 2002, curs on-line.
 Assessment The examination consists of written exam with the subject from all the matter (70%). In the final marks will be considered the activity in the framework of seminaries, where some short tests will be accomplished (30%).