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Elemente computat , ionale de deduct , ie logic˘a 27

9. ∂T = {n 5 , n 7 , n 10 , n 11 } ; toate vˆarfurile aflate pe frontiera arborelui curent generat au ca
etichete secvent , i axiom˘a, deci procesul de reactualizare a arborelui T se ˆıncheie cu decizia
Secventul init ,ial S este secvent demonstrabil.

Concluzii

Lucrarea prezint˘a pe lˆang˘a elementele de baz˘a ale unui limbaj de calcul cu propozit , ii logice
cu definirea conectivelor logice s , i a modului de reprezentare s , i o modalitate de determinare a
demostrabilit˘at , ii unei mult , imi de formule logice pe baza unei alte mult , imi logice prin utilizarea
regulilor de inferent , ˘a Gentzen. Algoritmul ce stabiles , te deduct , ia logic˘a a unui set de formule
logice ˆın funct , ie de informat , ii logice cunoscute este bazat pe regulile de inferent , ˘a Gentzen.
Prin descrierea teoretic˘a a elementelor de logic˘a matematic˘a s , i aplicarea unui rat , ionament
logic algoritmic cu aplicat , ii uzuale privind demonstrarea logic˘a automat˘a se arat˘a utilitatea s , i
caracterul aplicativ ˆın diverse domenii ce refer˘a reprezentarea cunos , tint , elor ˆıntr-un limbaj logic.

Bibliografie

[1] J.L. Bell, M. Machover, A Course in Mathematical Logic, North-Holland, 1997.

[2] M. Ben-Ari, Mathematical Logic for Computer Science, Springer Verlag, 2001.

[3] J. Bessie, S. Glennan, Elements of Deductive Inference: An Introduction to Symbolic Logic,
Wadsworth Publishing Company, 1999.

[4] C.M. Bishop, Neural Network for Pattern Recognition, Clarendon Press, 1995.

[5] A. Church, Introduction to Mathematical Logic, Princeton University Press, 1996.

[6] A. Cichocki, R. Unbehauen, Neural Networks for Signal Processing and Optimization, Wiley,
1994.

[7] T.M. Cover, J.A. Thomas, Elements of Information Theory, Wiley, 1991.

[8] K.I. Diamantaras, S.Y. Kung, Principal Component Neural Networks: Theory and Applica-
tions, Wiley, 1996.

[9] H.D. Ebbinghauss, J. Flum, W. Thomas, Mathematical Logic, Springer Verlag, 1994.

[10] M. Fitting, First-Order Logic and Automated Theorem Proving, Springer Verlag, 1996.

[11] T. Foster, Logic, Computation and Set Theory, CRC Press, 2002.

[12] M. Gabbay, C.J. Hogger, J.A. Robinson, Handbook of Logic in Artificial Intelligence and
Logic Programming, Oxford University Press, 1998.

[13] J.H. Gallier, Logic for Computer Science: Foundations of Automatic Theorem Proving,
Harper&Row, 2003.

[14] W. Gardner, Introduction to Random Processes with Applications to Signal and Systems,
Macmillan, 1986.

[15] R. Gonzalez, P. Wintz, Digital Image Processing, Addison-Wisley, 1987.