Grigore C. Moisil (1906 - 1973) and his School in Algebraic Logic
Keywords:
n-valued Lukasiewicz-Moisil algebra, q -valued Lukasiewicz-Moisil algebra, Post algebraAbstract
We present in the paper a very concise but updated survey emphasizing the research done by Gr. C. Moisil and his school in algebraic logic.
References
A. Amroune, Representation des algèbres de Åukasiewicz q -valentes involutives par des structures floues, BUSEFAL (Institut de Recherche en Informatique de Toulouse), 43, 1990, 5-11.
M. Abad, Three valued Åukasiewicz algebras with an additional operation, Rev. Union Mat. Argentina, 32, 1985, 107-117.
M. Abad, A. Figallo, Characterization of three-valued Åukasiewicz algebras, Rep. Math. Logic, 18, 1984, 47-59.
M. Abad, L. Monteiro, On three-valued Moisil algebras, Logique et Analyse, 27, 1984, 407-414.
I. B˘adele, V. Boicescu, Sur les extensions des algèbres de Åukasiewicz, C.R. Acad. Sci. Paris, 269, 1969, 313-315.
D. Becchio, Axiomatisation d'une logique trivalente Åukasiewiczienne, 1971, Manuscript.
D. Becchio, Nouvelle démonstration de la complétude du système de Wajsberg axiomatisant la logique trivalente de Åukasiewicz, C.R. Acad. Sci. Paris, 275, 1972, 679-681.
D. Becchio, Sur les définitions des algèbres trivalentes de Åukasiewicz donées par A. Monteiro, Logique et Analyse, 63-64, 1973, 339-344.
D. Becchio, Algèbres de Heyting, algèbres de Brouwer et algèbres trivalentes de Åukasiewicz, Logique et Analyse, 21, 1978, 237-248.
D. Becchio, Logique trivalente de Åukasiewicz, Ann. Sci., Univ. Clermont-Ferrand, 16, 1978, 38-89.
D. Becchio, L. Iturrioz, Sur une définition des algèbres de Åukasiewicz et de Post d'ordre n, Demonstratio Math., 11, 1978, 1083-1094.
L. Beznea, q -valued Moisil algebras and dual categories (Romanian), Master Thesis, University of Bucarest, 1981.
V. Boicescu, Sur la représentation des algèbres de Åukasiewicz q -valentes, C.R. Acad. Sci. Paris, 270, 1970, 4-7.
V. Boicescu, Sur les algèbres de Åukasiewicz, Logique,Automatique, Informatique, Editions de l'Academie de la R.S.Roumanie, 1971, 71-89.
V. Boicescu, Sur les systèmes déductifs dans la logique q -valente, Publ. Dép. Math. Lyon, 8, 1971, 123-133.
V. Boicescu, On Åukasiewicz algebras (Romanian), In: Probleme de logic˘a, vol.IV, Ed. Academiei R.S.Romania, Bucharest, 1972, 245-276.
V. Boicescu, On q -valued logics (Romanian), In: Probleme de Logic˘a, vol. V, 1973, Edit. Acad. R.S.Romania, 241-255.
V. Boicescu, Sur une logique polivalente, Rev. Roum. Sci. Soc., sér. Philos. et Logique, 17, 1973, 393-405.
V. Boicescu, Researches in Åukasiewicz algebras, Rev. Roum. Sci. Soc., sér. Philos. et Logique, 20, 1976, 197-200.
V. Boicescu, Extensions of homomorphisms of Lulasiewicz algebras with bounding semimorphisms, Rev. Roum. Sci. Soc., sér. Philos et Logique, 23, 1979, 367-370.
V. Boicescu, Contributions to the study of Åukasiewicz algebras (Romanian), Ph.D. Thesis, University of Bucharest, 1984.
V. Boicescu, Irredundant n-valued Moisil algebras, Discrete Math., 71, 1988, 197-204. http://dx.doi.org/10.1016/0012-365X(88)90100-8
V. Boicescu, G. Georgescu, Les algèbres de Åukasiewicz centrées et axées, Rev. Roum. Math. Pures et Appl., 15, 1970, 675-681.
V. Boicescu, A. Iorgulescu, Current research in the field of Åukasiewicz-Moisil algebras (Romanian), Studii Cerc. Mat., 39, 1987, 97-106.
V. Boicescu, A. Filipoiu, G. Georgescu, S. Rudeanu, Åukasiewicz-Moisil algebras, Annals of Discrete Mathematics, 49, 1991, North-Holland.
C.C. Chang, Algebraic analysis of many valued logics, Trans. Amer. Math. Soc., 1958, 88, 467-490. http://dx.doi.org/10.1090/S0002-9947-1958-0094302-9
R. Cignoli, Boolean elements in Åukasiewicz algebras. I. Proc. Japan Acad., 41, 1965, 670-675. http://dx.doi.org/10.3792/pja/1195522292
R. Cignoli, Un teorema de representation para algebras de Åukasiewicz trivalentes, Rev. Union Mat. Argentina, 23, 1966, 41.
R. Cignoli, Algebras de Moisil de orden n, Ph.D. Thesis, Universidad Nacional del Sur, Bahia Blanca, 1969.
R. Cignoli, Moisil algebras, Notas de Logica Matematica, Inst. Mat., Univ. National del Sur, Bahia-Blanca, No. 27, 1970.
R. Cignoli, Representation of Åukasiewicz algebras and Post algebras by continuous functions, Colloq. Math. 24, 1972, 127-138.
R. Cignoli, Topological representation of Åukasiewicz and Post algebras, Notas de Logica Matematica, Inst. Mat. Univ. National del Sur, Bahia-Blanca, No. 33, 1974.
R. Cignoli, Coproducts in the categories of Kleene and three-valued Åukasiewicz algebras, Studia Logica, 39, 1979, 237-245. http://dx.doi.org/10.1007/BF00405382
R. Cignoli, Proper n-Valued Åukasiewicz Algebras as S-Algebras of Åukasiewicz n-Valued Propositional Calculi, Studia Logica, 41, 1982, 3-16. http://dx.doi.org/10.1007/BF00373490
R. Cignoli, An algebraic approach to elementary theories based on n-valued Åukasiewicz logics, Z. Math. Logik u. Grundl. Math., 30, 1984, 87-96. http://dx.doi.org/10.1002/malq.19840300106
R. Cignoli, M.S. De Gallego, The lattice structure of 4-valued Åukasiewicz algebras, J. Symbolic Logic, 46, No. 1, 1981, 185.
R. Cignoli, M.S. De Gallego, The lattice structure of some Åukasiewicz algebras, Algebra Universalis, 13, 1981, 315-328. http://dx.doi.org/10.1007/BF02483844
R. Cignoli, A. Monteiro, Boolean elements in Åukasiewicz algebras. II., Proc. Japan Acad., 41, 1965, 676- 680. http://dx.doi.org/10.3792/pja/1195522293
R. Cignoli and D. Mundici, An elementary proof of Chang's completeness theorem for the infinite-valued calculus of Åukasiewicz, Studia Logica, to appear.
R. Cignoli, I.M.L. D'Ottaviano, D. Mundici, Algebraic Foundations of many-valued Reasoning, Kluwer 2000, Volume 7. http://dx.doi.org/10.1007/978-94-015-9480-6
J. Coulon, J.L. Coulon, A propos de la représentation des algèbres de Åukasiewicz et des algèbres booléiennes floues, Rev. Roum. Math. Pures et Appl., 34, 1989, 403-411.
J. Coulon, J.L. Coulon, Un nouveau resultat concernant la representation d'une algèbre de Åukasiewicz involutive dans l'algèbre des parties floues d'une structure floue involutive, Rev. Roumaine Math. Pures et Appl., 38, 1993, 319-326.
A. Figallo, J. Tolosa, Algebras de Åukasiewicz trivalente, Univ. Nac. de San Juan, 1982.
A. Figallo Jr., M. Figallo and A. Ziliani, Free (n+1)-valued Åukasiewicz BCK algebras, Demonstratio Mathematica, XXXVII, 2, 2004, 245-254.
A.V. Figallo, I. Pascual, A. Ziliani, Notes on monadic n-valued Åukasiewicz algebras, Math. Bohem., 3, 129, 2004, 255-271.
A.V. Figallo, C. Sanza , A. Ziliani, Functional monadic n-valued Åukasiewicz algebras, accepted by Mathematica Bohemica.
A.V. Figallo, I. Pascual, A. Ziliani, Subdirectly irreducible monadic Åukasiewicz-Moisil algebras, Manuscript.
A.V. Figallo, Åukasiewicz BCK-algebras endowed with Moisil operators, Manuscript.
A.V. Figallo, A. Figallo Jr., M. Figallo, A. Ziliani, Åukasiewicz residuation algebras with infimum, Manuscript.
A. Filipoiu, Analytic tableaux for q -valued propositional logic, Math. Seminar Notes, 6, 1978, 517-526.
A. Filipoiu, Representation theorems for Åukasiewicz algebras, Discrete Math., 27, 1979, 107-110. http://dx.doi.org/10.1016/0012-365X(79)90075-X
A. Filipoiu, Representation of Åukasiewicz algebras by means of ordered Stone spaces, Discrete Math., 30, 1980, 111-116. http://dx.doi.org/10.1016/0012-365X(80)90112-0
A. Filipoiu, q -valued Åukasiewicz-Moisil algebras and logics (Romanian), Ph.D. Thesis, Univ. of Bucharest, 1981.
A. Filipoiu, Representation theorems for q -valued Åukasiewicz algebras, Discrete Math., 33, 1981, 21-27. http://dx.doi.org/10.1016/0012-365X(81)90254-5
A. Filipoiu, Some remarks on the representation theorem of Moisil, Discrete Math., 33, 1981, 163-170. http://dx.doi.org/10.1016/0012-365X(81)90163-1
J. M. Font, A. J. Rodriguez, A. Torrens, Wajsberg Algebras, Stochastica, VIII, 1, 5-31, 1984.
G. Georgescu, Algébres de Åukasiewicz complètes, C.R. Acad. Sci. Paris, 269, 1969, 1181-1184.
G. Georgescu, The centered epimorphisms and the construction of the tensor product in Åuk, Rev. Roum. Math. Pures Appl., 15, 1970, 693-709.
G. Georgescu, n-valued complete Åukasiewicz algebras, Rev. Roum. Math. Pures Appl., 16, 1971, 41-50.
G. Georgescu, The q -valued Åukasiewicz algebras. I., Rev. Roum. Math. Pures Appl., 16, 1971, 195-209.
G. Georgescu, Algebras de Åukasiewicz de orden q . II., Rev. Roum. Math. Pures Appl., 16, 1971, 363-369.
G. Georgescu, Les algèbres de Åukasiewicz q -valentes, In: Logique, Automatique, Informatique, Edit. Acad. R.S.Romania, Bucharest, 1971, 99-169.
G. Georgescu, The q -valued Åukasiewicz algebras. III. Duality theory., Rev. Roum. Math. Pures Appl., 16, 1971, 1365-1390.
G. Georgescu, Algebre Åukasiewicz q -valente, Ph.D. Thesis, Math. Institute, Bucharest, mai 1972.
G. Georgescu, Représentation des algèbres de Åukasiewicz q -valentes polyadiques, C. R. Acad. Sci. Paris, A-B, 274, 1972, A944-A946.
G. Georgescu, Reprezentarea algebrelor Åukasiewicz poliadice local finite de grad infinit, Studii Cerc. Mat., 24, 1972, 1107-1117.
G. Georgescu, Some remarks on the polyadic Åukasiewicz algebras, Rev. Roum. Mat. Pures Appl., 22, 1977, 641-648.
G. Georgescu, On the homogeneous-universal Åukasiewicz algebras, Rev. Roum. Mat. Pures Appl., 23, 1978, 29-32.
G. Georgescu, A. Iorgulescu, Pseudo-MV Algebras: a Noncommutative Extension of MV Algebras, The Proceedings of the Fourth International Symposium on Economic Informatics, Bucharest, Romania, May 1999, 961-968.
G. Georgescu, I. Leuștean, Towards a probability theory based on Moisil logic, Soft Computing, 2000, 4, No.1, 19-26. http://dx.doi.org/10.1007/s005000050076
G. Georgescu, A. Iorgulescu, Pseudo-BL algebras: A noncommutative extension of BL algebras, Abstracts of The Fifth International Conference FSTA 2000, Slovakia, February 2000, 90-92.
G. Georgescu, A. Iorgulescu, Pseudo-BCK algebras: An extension of BCK algebras, Proceedings of DMTCS'01: Combinatorics, Computability and Logic, Springer, London, 2001, 97-114. http://dx.doi.org/10.1007/978-1-4471-0717-0_9
G. Georgescu, I. LeuÈ™tean, Probabilities on Åukasiewicz-Moisil algebras, International Journal of Approximate Reasoning, 1998, 18, No.3-4, 201-215. http://dx.doi.org/10.1016/S0888-613X(98)00006-1
G. Georgescu, I. LeuÈ™tean, Conditional probabilities on Åukasiewicz-Moisil algebras, Analele Universitatii Bucuresti, 1998, 47, 55-64.
G. Georgescu., I. LeuÈ™tean, A. Popescu, Order convergence and distance on Åukasiewicz-Moisil algebras, Multiple Valued Logic, to appear.
G. Georgescu, A. Popescu, A common generalization for algebras and Åukasiewicz-Moisil algebras, submitted.
G. Georgescu, C. Vraciu, Le spectre maximal dÅ une algèbre de Åukasiewicz, C.R. Acad. Sci. Paris, 268, 1969, 928-929.
G. Georgescu, C. Vraciu, n-valued centered Åukasiewicz algebras, Rev. Roum. Math. Pures Appl., 14, 1969, 712-723.
G. Georgescu, C. Vraciu, Sur les algèbres de Åukasiewicz centrées, C.R. Acad. Sci. Paris, 268, 1969, 998- 1000.
G. Georgescu, C. Vraciu, Sur le spectre maximal d'une algèbre de Åukasiewicz, Publ. Dép. Math. Lyon, 6, 1969, 42-54.
G. Georgescu, C. Vraciu, Sur les épimorphismes centrées des algèbres de Åukasiewicz, C.R. Acad. Sci. Paris,269, 1969, 4-6.
G. Georgescu, C. Vraciu, On the characterization of centered Åukasiewicz algebras, J. Algebra, 16, 1970, 486-495. http://dx.doi.org/10.1016/0021-8693(70)90002-5
G. Georgescu, C. Vraciu, Monadic Boolean algebras and monadic Åukasiewicz algebras (Romanian), Studii Cerc. Mat., 23, 1971, 1025-1048.
G. Georgescu, C. Vraciu, La dualité des algèbres de Post q -valentes, J. Algebra, 21, 1972, 74-86. http://dx.doi.org/10.1016/0021-8693(72)90035-X
H. Goldberg, H. Leblanc, G. Weaver, A strong completeness theorem for 3-valued logic, Notre Dame J. Formal Logic, 15,1974, 325-332. http://dx.doi.org/10.1305/ndjfl/1093891310
M. Greniewski, Using three valued logics in the theory of swiching theory (Romanian). I. Realizarea cu circuite a func¸tiilor fundamentale, Comunic. Acad. R.P.R., 6, 1956, 225-229.
R. Grigolia, Algebraic analysis of Åukasiewicz-Tarski's n-valued logical systems, in: Selected Papers on Åukasiewicz Sentential Calculi (R. Wójcicki and G. Malinowski, Eds.), Polish Acad. Of Sciences, Ossolineum, Wroclaw, 1977, 81-92.
A. Iorgulescu, On the construction of three-valued Åukasiewicz-Moisil algebras, Discrete Math., 47, 1984, 213-227. http://dx.doi.org/10.1016/0012-365X(84)90184-5
A. Iorgulescu, Functors between categories of three-valued Åukasiewicz-Moisil algebras, Discrete Math., 49, 1984, 121-131. http://dx.doi.org/10.1016/0012-365X(84)90109-2
A. Iorgulescu, (1+q )-valued Åukasiewicz-Moisil algebras with negation (Romanian), Ph.D. Thesis, Univ. of Bucharest, 1984.
A. Iorgulescu, Connections between MVn algebras and n-valued Åukasiewicz-Moisil algebras - I, Discrete Mathematics, 181 (1-3), 1998, 155-177. http://dx.doi.org/10.1016/S0012-365X(97)00052-6
A. Iorgulescu, Connections between MVn algebras and n-valued Åukasiewicz-Moisil algebras - II, Discrete Mathematics, 202, 1999, 113-134. http://dx.doi.org/10.1016/S0012-365X(98)00289-1
A. Iorgulescu, Connections between MVn algebras and n-valued Åukasiewicz-Moisil algebras -III, Manuscript.
A. Iorgulescu, Connections between MVn algebras and n-valued Åukasiewicz-Moisil algebras - IV, Journal of Universal Computer Science, vol. 6, no I, 2000, 139-154.
L. Iturrioz, Axiomas para el calculo proposicional trivalente de Åukasiewicz, Rev. Union Mat. Argentina, 22, 1965, 150.
L. Iturrioz, Sur une classe particulière d'algèbres de Moisil, C. R. Acad. Sci. Paris, 267, 1968, 585-588.
L. Iturrioz, Les algèbres de Heyting-Brouwer et de Åukasiewicz trivalentes, Notre Dame J. Formal Logic, 17, 1976, 119-126. http://dx.doi.org/10.1305/ndjfl/1093887429
L. Iturrioz, Algèbres de Åukasiewicz symétriques, Publ. Dép. Math. Lyon, 13, 1976, 73-96.
L. Iturrioz, Åukasiewicz and symmetrical Heyting algebras, Z. Math. Logik u. Grund.Math., 23, 1977, 131- 136. http://dx.doi.org/10.1002/malq.19770230706
L. Iturrioz, Two characteristic properties of monadic three-valued Åukasiewicz algebras, Rep. Math. Logic, 8, 1977, 63-68.[101] L. Iturrioz, An axiom system for three-valued Åukasiewicz propositional calculus, Notre Dame J. Formal Logic, 18, 1977, 616-620.
L. Iturrioz, An axiom system for three-valued Åukasiewicz propositional calculus, Notre Dame J. Formal Logic, 18, 1977, 616-620. http://dx.doi.org/10.1305/ndjfl/1093888131
L. Iturrioz, O. Rueda, Algèbres implicatives trivalentes de Åukasiewicz libres, Discrete Math., 18, 1977, 35-44. http://dx.doi.org/10.1016/0012-365X(77)90004-8
I. LeuÈ™tean, A unifying framework for Åukasiewicz-Moisil algebras, MV-algebras and Post algebras, submitted.
J. Åukasiewicz, On three-valued logic (Polish), Ruch Filozoficzny, 5, 1920, 160-171.
J. Åukasiewicz, Philosophische Bemerkungen zur mehrwertigen Systemen des Aussagenkalküls, C.R. Séances Soc. Sci. Lettres Varsovie, Cl. III, 23, 1930, 51-77. Romanian translation in: Logic˘a È™i Filozofie, Ed. Politic˘a, BucureÈ™ti, 1966, 295-320.
J. Åukasiewicz, Die Logik und das Grundlagenproblem, Les entretiens de Zurich sur les fondements et la méthode des sciences mathématiques, 1941, 88-100.
J. Åukasiewicz, A. Tarski, Untersuchungen über den Aussagenkalkül, C.R. Séances Soc. Sci. Lettres Varsovie, Cl. III, 23, 1930, 30-50.
M.G. Malinowski, n-valued Åukasiewicz algebras and their connection to Post algebras of order (Polish), Zeszyty Naukowe u.t., Filozofia, 1972.
P. Mangani, On certain algebras related to many-valued logics (Italian), Boll. Un. Mat. Ital. (4) 8, 68-78, 1973.
W. Marek, T. Traczyk, Generalized Åukasiewicz algebras, Bull. Acad. Polonaise Sci. Sér. Math. Astronom. Phys., 17, 1969, 789-792.
Gr. C. Moisil, Recherches sur l'algèbre de la logique, Ann. Sci. Univ. Jassy, 22, 1935, 1-117.
Gr. C. Moisil, Sur le mode problématique, C.R. Séances Acad. Sci. Roumanie, 2, No. 2, 1938, 101-103.
Gr. C. Moisil, Recherches sur les logiques non-chrysippiennes, Ann. Sci. Univ. Jassy, 26, 1940, 431-466.
Gr.C. Moisil, Notes sur les logiques non-chrysippiennes, Ann. Sci, Univ. Jassy, 27, 1941, 86-98.
Gr. C. Moisil, Sur les anneaux de caractéristique 2 ou 3 et leurs applications, Bul. Politechn. Bucharest, 12, 1941, 66-90.
Gr. C. Moisil, Contributions à l'étude des logiques non-chrysippiennes. I. Un nouveau système d'axiomes pour les algèbres Åukasiewicziennes tétravalentes, C.R. Acad. Sci. Roumanie, 5, 1941, 289-293.
Gr. C. Moisil, Contributions à l'étude des logiques non-chrysippiennes. II. Anneaux engendrés par les algèbres Åukasiewicziennes centrées, C.R. Acad. Sci. Roumanie, 6, 1942, 9-14.
Gr. C. Moisil, Contributions à l'étude des logiques non-chrysippiennes. III. Anneaux engendrés par les algèbres Åukasiewicziennes tétravalentes axées, C.R. Acad. Sci. Roumanie, 7, 1942, 14-18.
Gr. C. Moisil, Logique modale, Disquis. Math. Phys., 2, 1942, 3-98.
Gr. C. Moisil, The algebra of networks with rectifiers (Romanian), Rev. Univ. C.I. Parhon și a Politehnicii București, 4-5, 1954, 9-41.
Gr. C. Moisil, Utilization of three-valued logics in the theory of switching circuits. II. The characteristic equation of a relay. III. Actual-contact circuits. IV. Realization of the working functions in actual operation (Romanian). Comun. Acad. R.P. Române, 6, 1956, 231-239, 385-386, 971-973.
Gr. C. Moisil, Applications of three-valued logics to the study of actual operation of relay-contact circuits (Romanian), Bul. Mat. Soc. St. Fiz. R.P. Române, 1(49), 1957, 147-191.
Gr. C. Moisil, Utilization of three-valued logics to the theory of switching circuits. V. P-I circuits (Romanian), Comunic. Acad. R.P. Române, 8, 1958, 1127-1128.
Gr. C. Moisil, Utilization of three-valued logics to the theory of switching circuits. VI. Polarized relays with unstable neutral. VII. Operation of ordinary relays under low self-maintaining current. VIII. -twoterminals with contacts and resistances. IX. -two-terminals with contacts, valves and resistances. X. Physical interpretation of the characteristic function of a multiterminal (Romanian), Comunic. Acad. R.P. Române, 9, 1959, 411-413, 531-532, 533-535, 665-666, 667-669.
Gr. C. Moisil, Sur l'application de la logique à trois valeurs à l'étude des circuits électriques à contacts, redresseurs et résistances, Rev. Math. Pures Appl., 4, 1959, 173-183.
Gr. C. Moisil, The algebraic Theory of Switching Circuits (Romanian), Ed. Tehnic˘a București. English translation 1969, Pergamon Press, Oxford, and Editura Tehnic˘a București.
Gr.C. Moisil, Sur les idéaux des algèbres Åukasiewicziennes trivalentes, Analele Univ. C.I. Parhon, Seria Acta Logica, 3, 1960, 83-95.
Gr.C. Moisil, On predicate calculus in three-valued logics (Russian), An. Univ. C.I. Parhon, Acta Logica, 4, 1961, 103-112.
Gr.C. Moisil, Sur la logique à trois valeurs de Åukasiewicz, An. Univ. C.I. Parhon, Acta Logica, 5, 1962, 103-117.
Gr.C. Moisil, Les logiques non-chrysippiennes et leurs applications, Acta Philos. Fennica, 16, 1963, 137- 152.
Gr.C. Moisil, Le algèbre di Åukasiewicz, An. Univ. C.I. Parhon, Acta Logica 6, 1963, 97-135.
Gr.C. Moisil, Applicazioni dell'algebra alle calcolatrici moderne, Atti Reunione del Groupement des Math. D'Expression Latine, 26.IX-3.X. 1961, Ed. Cremonese, Roma, 1963.
Gr.C. Moisil, The interest of the actual operation of switching circuits for the logician, An. Univ. București, Acta Logica, 7-8, 1964, 131-139.
Gr.C. Moisil, Sur les logiques de Åukasiewicz à un nombre fini de valeurs, Rev. Roum. Math. Pures Appl., 9, 1964, 905-920.
Gr.C. Moisil, Încerc˘ari vechi și noi de logic˘a neclasic˘a (Old and New Essays on Non-Classical Logics), Edit.¸ Stiin¸tific˘a, Bucharest, 1965.
Gr.C. Moisil, Théorie structurelle des automats finis, Gauthiers-Villars, Paris, 1967.
Gr.C. Moisil, Åukasiewiczian algebras, Computing Center, University of Bucharest (preprint), 311-324, 1968.
Gr.C. Moisil, Essais sur les logiques non-chrysippiennnes, Ed. Academiei R.S.R., Bucharest, 1972.
Gr.C. Moisil, Ensembles flous et logiques à plusieurs valeurs, Centr. Rech. Math., Université de Montréal, mai, 1973 (preprint).
Gr.C. Moisil, Lec¸tii despre logica ra¸tionamentului nuan¸tat (Lectures on the Logic of Fuzzy Reasoning), Ed. ¸ Stiin¸tific˘a și Enciclopedic˘a, Bucharest, 1975.
Gr.C. Moisil, Sur l'emploi des mathématiques dans les sciences de l'homme, Accad. Naz. Lincei, Contributi del Centro Linceo Interdisciplinare di Sci. Mat. E loro Appl., No. 17, 1976.
A. Monteiro, Matrices de Morgan caracteristiques pour le calcul propositional classique, Ann. Acad. Brasil, 52, 1960, 1-7.
A. Monteiro, Sur la définition des algèbres de Åukasiewicz trivalentes, Notas de Logica matematica, 21, 1964.
A. Monteiro, Construction des algèbres de Åukasiewicz trivalentes dans les algèbres de Boole monadiques, Notas de Logica Matematica, 11, 1964.
A. Monteiro, R. Cignoli, Construccion geometrica de las algebras de Åukasiewicz trivalentes libres, Rev. Union Mat. Argentina, 22, 1965, 152-153.
L. Monteiro, Axiomes indépendentes pour les algèbres de Åukasiewicz trivalentes, Notas de Logica Matematica, 32, 1974.
L. Monteiro, Algebras de Åukasiewicz trivalentes monadicas, Notas de Logica Matematica, 32, 1974.
L. Monteiro, Sur la construction L des algèbres de Åukasiewicz trivalentes, Rev. Roum. Math. Pures Appl., Tome XXIII, No. 1, 1978, 77-83.
L. Monteiro, L.G. Coppola, Sur une construction des algèbres de Åukasiewicz trivalentes, Notas de Logica Matematica, 17, 1964.
D. Mundici, MV-algebras are categorically equivalent to bounded commutative BCK-algebras, Math. Japonica, 31, No. 6, 1986, 889-894.
D. Mundici, Interpretation of AF C?-algebras in Åukasiewicz sentential calculus, J. Funct. Anal., 65, 1986, 15-63. http://dx.doi.org/10.1016/0022-1236(86)90015-7
D. Mundici, The C¤-algebras of three-valued logic, Logic Colloquium'88, Ferro, Bonotto, Valentini and Zanardo (Editors), Elsevier Science Publishers B.V. (North-Holland), 1989, 61-77.
Gh. Nadiu, On a method for the construction of three-valued Åukasiewicz algebras (Romanian), Studii Cerc. Mat., 19, 1967, 1063-1070.
A. Petcu, The definition of the trivalent Åukasiewicz algebras by three equations, Rev. Roumaine Math. Pures Appl., 13, 1968, 247-250.
I. Petrescu (I. Voiculescu), Injective objects in the category of De Morgan algebras, Rev. Roumaine Math. Pures Appl., 16, 1971, 921-926.
D. Ponasse, Algèbres floues et algèbres de Åukasiewicz, Rev. Roumaine Math. Pures Appl., XXIII, 1, 1978, 103-111.
E. Post, Introduction to a general theory of elementary propositions, Amer. J. Math., 43, 1921, 163-185. http://dx.doi.org/10.2307/2370324
E. Radu, L'oeuvre de Gr. C. Moisil en logique mathématique, I., II., Rev. Roumaine Math. Pures Appl., 23, 1978, 463-477, 605-610.
J. Rodriguez, A. Torrens, Wajsberg Algebras and Post Algebras, Studia logica, 53, 1994, 1-19. http://dx.doi.org/10.1007/BF01053019
P. Rosenbloom, Post algebras. I. Postulates and general theory, Amer. J. Math., 64, 1942, 167-183. http://dx.doi.org/10.2307/2371676
S. Rudeanu, On Åukasiewicz-Moisil algebras of fuzzy sets, Studia Logica, 52, 1993, 95-111. http://dx.doi.org/10.1007/BF01053066
A. Sade, Algèbres de Åukasiewicz dans la logique trivalente, Univ. Beograd, Publ. Elektrotehn. Fak. Ser. Mat. Fiz., No. 247-273, 1969, 123-130.
C. Sanza, Notes on n£m-valued Åukasiewicz algebras with negation, L. J. of the IGPL, 6, 12, 2004, 499-507 (<http://jigpal.oupjournals.org/current.dtl>)
C. Sanza, Monadic n£m-valued Åukasiewicz algebras with negation, Manuscript.
C. Sicoe, Strictly chrysippian elements in many-valued Åukasiewicz algebra (Romanian), An. Univ. of Bucharest, 15, 1966, 123-126.
C. Sicoe, Sur les ideaux des algèbres Åukasiewicziennes polivalentes, Rev. Roum. Math. Pures Appl., 12, 1967, 391-401.
C. Sicoe, Note asupra algebrelor Åukasiewicziene polivalente, Stud. È™i Cerc. Mat., 19, 1967, 1203-1207.
C. Sicoe, On many-valued Åukasiewicz algebras, Proc. Japan Acad., 43, 1967, 725-728. http://dx.doi.org/10.3792/pja/1195521470
C. Sicoe, A characterization of Åukasiewicz algebras. I. II. Proc. Japan Acad., 43, 1967, 729-732, 733-736.
C. Sicoe, Sur la définition des algèbres Åukasiewicziennes polyvalentes, Rev. Roumaine Math. Pures Appl., 13, 1968, 1027-1030.
W. Suchon, On the non-equivalence of two definitions of the algebra of Åukasiewicz, P Polish Acad. Sci. Inst. Philos. Sociol. Bull. Sect. Logic, 1, No. 1, 1972, 35-37.
W. Suchon, Inéquivalence de certaines définitions des algèbres infinites de Åukasiewicz, Rep. Math. Logic, 1, 1973, 21-26.
W. Suchon, On defining Moisil's functors in n-valued Åukasiewicz propositional logic, Polish Acad. Sci. Inst. Philos. Sociol. Bull. Sect. Logic, 2, 1973, 195-196.
W. Sucho’n, Définition des foncteurs modaux de Moisil dans le calcul n-valent des propositions de Åukasiewicz avec implication et négation, Reports on Mathematical Logic 2, 43-48, 1974.
W. Suchon, Matrix Åukasiewicz algebras, Rep. Math. Logic, 4, 1975, 91-104.
W. Suchon, Définition des foncteurs modaux de Moisil dans le calcul n-valent des propositions de Åukasiewicz avec implication et négation, Reports on Mathematical Logic, 2, 1974, 43-48.
J. Varlet, Algèbres de Åukasiewicz trivalentes, Bull. Soc. Roy. Sci. Liège, 36, 1968, 399-408.
J. Varlet, Considérations sur les algèbres de Åukasiewicz trivalentes, Bull. Soc. Roy. Sci. Liège,38, 1969, 462-469.
M.Wajsberg, Axiomatization of three-valued propositional calculus (Polish), C.R. Séances Soc. Sci. Lettres Varsovie, Cl. III, 24, 1931, 126-145.
R. Wójcicki, A theorem on the finiteness of the degree of maximality of the n-valued Åukasiewicz logic, Polish Acad. Sci. Inst. Philos. Sociol. Bull. Sect. Logic, 4, 1975, 19-25.
R. Wójcicki, G. Malinowski (editors), Selected Papers on Åukasiewicz sentencial calculi, Ossolineaum, Wroclaw and Warsaw, 1977.
L.A. Zadeh, Fuzzy Sets, Inform. And Control, 8, 1965, 338-353. http://dx.doi.org/10.1016/S0019-9958(65)90241-X
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