Czasopismo
2004
|
Vol. 63, nr 4
|
357--373
Tytuł artykułu
Autorzy
Wybrane pełne teksty z tego czasopisma
Warianty tytułu
Języki publikacji
Abstrakty
Several algebraic structures (namely HW, BZMVdM, Stonean MV and MVΔ algebras) related to many valued logical systems are considered and their equivalence is proved. Four propositional calculi whose Lindenbaum-Tarski algebra corresponds to the four equivalent algebraic structures are axiomatized and their semantical completeness is given.
Słowa kluczowe
Czasopismo
Rocznik
Tom
Strony
357--373
Opis fizyczny
Bibliogr. 18 poz.
Twórcy
autor
- Dipartimento di Informatica, Sistemistica e Communicazione, Universita degli Studi di Milano-Bicocca, Via Bicocca degli Arcimboldi 8, 20126 Milano, Italy, cattang@disco.unimib.it
autor
- Dipartimento di Informatica, Sistemistica e Communicazione, Universita degli Studi di Milano-Bicocca, Via Bicocca degli Arcimboldi 8, 20126 Milano, Italy, ciucci@disco.unimib.it
autor
- Dipartimento di Scienze Pedagogiche e Filosofiche, Università di Cagliari, Via Is Mirrionis 1, 09123 Cagliari, Italia, giuntini@unica.it
autor
- Dipartimento di Scienze Pedagogiche e Filosofiche, Università di Cagliari, Via Is Mirrionis 1, 09123 Cagliari, Italia, martinvk@iol.it
Bibliografia
- [1] Belluce, L. P.: Generalized fuzzy connectives onMV-algebras, J. Math. Anal. Appl., 206(1), 1997, 485-499.
- [2] Birkhoff, G.: Lattice Theory, vol. XXV of American Mathematical Society Colloquium Publication, Third edition, American Mathematical Society, Providence, Rhode Island, 1967.
- [3] Cattaneo, G., Ciucci, D.: BZW algebras for an abstract approach to roughness and fuzziness, IPMU 2002, July 1-5 2002, Annecy, France, Proceedings, ESIA - Université de Savoie, 2002.
- [4] Cattaneo, G., Ciucci, D.: Heyting Wajsberg algebras as an abstract environment linking fuzzy and rough sets, Lecture Notes in Artificial Intelligence, 2475, 2002, 77-84.
- [5] Cattaneo, G., Ciucci, D., Giuntini, R., Konig, M.: Algebraic Structures Related to Many Valued Logical Systems. Part I: Heyting Wajsberg Algebras, Fundamenta Informaticae, 2004, Accepted.
- [6] Cattaneo, G., Dalla Chiara, M. L., Giuntini, R.: Some Algebraic Structures for Many-Valued Logics, Tatra Mountains Mathematical Publication, 15, 1998, 173-196, Special Issue: Quantum Structures II, Dedicated to Gudrun Kalmbach.
- [7] Cattaneo, G., Giuntini, R., Pilla, R.: BZMV__ and Stonian MV algebras (Applications to fuzzy sets and rough approximations), Fuzzy Sets Syst., 108, 1999, 201-222.
- [8] Cattaneo, G., Lombardo, F.: Independent axiomatization of MV-algebras, Tatra Mountains Mathematical Publication, 15, 1998, 227-232, Special Issue: Quantum Structures II, Dedicated to Gudrun Kalmbach.
- [9] Chang, C. C.: Algebraic analysis of many valued logics, Trans. Amer. Math. Soc., 88, 1958, 467-490.
- [10] Cignoli, R., D’Ottaviano, I., Mundici, D.: Algebraic foundations of many-valued reasoning, Kluwer Academic, Dordrecht, 1999.
- [11] Esteva, F., Godo, L., Hájek, P., Navara,M.: Residuated Fuzzy logics with an involutive negation, Archive for Mathematical Logic, 39, 2000, 103-124.
- [12] Hájek, P.: Metamathematics of Fuzzy Logic, Kluwer, Dordrecht, 1998.
- [13] Konig, M.: Many-valued logics enriched with a Stonean negation: a direct proof of representation and completeness, 2004, Preprint.
- [14] Monteiro, A.: Axiomes Independants pour les Algebres de Brouwer, Revista de la Uni´on matematica Argentina y de la Asociaci´on Fisica Argentina, 17, 1955, 149-160.
- [15] Monteiro, A.: Sur Les Algèbres de Heyting symétriques, Portugaliae Mathematica, 39, 1980, 1-237.
- [16] Rasiowa, H., Sikorski, R.: The Mathematics of Metamathematics, vol. 41 of Monografie Matematyczne, Third edition, Polish Scientific Publishers, Warszawa, 1970.
- [17] Surma, S.: Logical Works, Polish Academy of Sciences, Wroclaw, 1977.
- [18] Turunen, E.: Mathematics Behind Fuzzy Logic, Physica-Verlag, Heidelberg, 1999.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.baztech-article-BUS2-0005-0104