Geodesic
Lukasiewicz's logic as an architecture model of arithmetic
Sibirskij žurnal industrialʹnoj matematiki, Tome 6 (2003) no. 4, pp. 32-50.

Voir la notice de l'article provenant de la source Math-Net.Ru

We obtain a complete formal description of various architecture models of computer realizations of arithmetic in terms of the finite-valued Lukasiewicz logic and logics enriched by it. The weak incompleteness property of these logics enables one to study the structural characteristics of operations independent of the representation of numbers, such as the forms of admissible overflows. We describe some properties of the lattice of these logics and find bases suitable for applications. We consider logical structures that arise in the realization of arithmetic operations and the representation of overflow in positional number systems. We indicate paths for the development of hardware-based realizations of arithmetic. We present a new view of the nature of Lukasiewicz's logic. 
@article{SJIM_2003_6_4_a2,
     author = {S. P. Kovalyov},
     title = {Lukasiewicz's logic as an architecture model of arithmetic},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {32--50},
     publisher = {mathdoc},
     volume = {6},
     number = {4},
     year = {2003},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2003_6_4_a2/}
}
TY  - JOUR
AU  - S. P. Kovalyov
TI  - Lukasiewicz's logic as an architecture model of arithmetic
JO  - Sibirskij žurnal industrialʹnoj matematiki
PY  - 2003
SP  - 32
EP  - 50
VL  - 6
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SJIM_2003_6_4_a2/
LA  - ru
ID  - SJIM_2003_6_4_a2
ER  - 
%0 Journal Article
%A S. P. Kovalyov
%T Lukasiewicz's logic as an architecture model of arithmetic
%J Sibirskij žurnal industrialʹnoj matematiki
%D 2003
%P 32-50
%V 6
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SJIM_2003_6_4_a2/
%G ru
%F SJIM_2003_6_4_a2
S. P. Kovalyov. Lukasiewicz's logic as an architecture model of arithmetic. Sibirskij žurnal industrialʹnoj matematiki, Tome 6 (2003) no. 4, pp. 32-50. http://geodesic.mathdoc.fr/item/SJIM_2003_6_4_a2/

[1] Yakobson A., Buch G., Rambo Dzh., Unifitsirovannyi protsess razrabotki programmnogo obespecheniya, Piter, SPb., 2002

[2] Kovalev S. P., “Analiticheskie modeli mashinnoi arifmetiki”, Sib. zhurn. industr. matematiki, 6:3 (2003), 88–102 | MR | Zbl

[3] Voevodin V. V., Voevodin Vl. V., Parallelnye vychisleniya, BKhV-Peterburg, SPb., 2002

[4] Yablonskii S. V., “Vvedenie v teoriyu funktsii $k$-znachnoi logiki”, Diskretnaya matematika i matematicheskie voprosy kibernetiki, T. 1, Nauka, M., 1974

[5] Evans T., Schwartz P. B., “On Slupecki $T$-functions”, J. Symbolic Logic, 23 (1958), 267–270 | DOI | MR

[6] Karpenko A. S., Logiki Lukasevicha i prostye chisla, Nauka, M., 2000 | MR

[7] Rosenberg I. G., “Completeness properties of multiple-valued logic algebras”, Computer Science and Multiple-Valued Logic, North-Holland, Amsterdam, 1977, 144–186

[8] McNaughton R., “A theorem about infinite valued sentential logic”, J. Symbolic Logic, 16 (1951), 1–13 | DOI | MR | Zbl

[9] Bochvar D. A., Finn V. K., “O mnogoznachnykh logikakh, dopuskayuschikh formalizatsiyu antinomii, 1”, Issledovaniya po matematicheskoi lingvistike, matematicheskoi logike i informatsionnym yazykam, Nauka, M., 1972, 238–295

[10] Bauer F. L., Gooz G., Informatika. Vvodnyi kurs, T. 1–2, Mir, M., 1990 | MR

[11] Epstein G., Frieder G., Rine D. C., “The development of multiple valued logic as related to computer science”, IEEE Computer, 1974, no. 7(9), 20–32

[12] Arestova M. L., Bykovskii A. Yu., “Metodika realizatsii optoelektronnykh skhem mnogoparametricheskoi obrabotki signalov na osnove printsipov mnogoznachnoi logiki”, Kvantovaya elektronika, 22:10 (1995), 980–984

[13] Onneweer S. P., Kerkhoff H. G., “High-radix current-mode CMOS circuits based on the truncated-difference operator”, 17 Internat. Symp. on Multiple-Valued Logic, Boston, 1987, 188–195

[14] Kuznetsov A. V., “O sredstvakh dlya obnaruzheniya nevyvodimosti i nevyrazimosti”, Logicheskii vyvod, Nauka, M., 1979, 5–33

[15] Evans J., Trimper G., Itanium Architecture for Programmers: Understanding 64-Bit Processors and EPIC Principles, Prentice Hall, Englewood Cliffs, 2003

[16] Beavers G., “Automated theorem proving for Lukasiewicz logics”, Studia Logica, 52:2 (1993), 183–195 | DOI | MR | Zbl

[17] Karpenko A. S., “Mnogoznachnye logiki”, Logika i kompyuter, no. 4, Nauka, M., 1997