|
Zapiski Nauchnykh Seminarov POMI, 2003, Volume 304, Pages 19–74
(Mi znsl877)
|
|
|
|
This article is cited in 2 scientific papers (total in 2 papers)
Formal axiomatic theories on the base of three-valued logic
I. D. Zaslavsky Institute for Informatics and Automation Problems of National Academy of Science of the Republic of Armenia
Abstract:
Formal axiomatic theories on the base of J. Lukasiewicz's three-valued logic are considered. Main notions connected with these theories are introduced, for example, the notion of a Luk-model (i.e., model of a theory in terms of J. Lukasiewicz's logic), of a Luk-consistent theory, Luk-complete theory. Logical calculi describing such theories are defined; analogues of the classical theorems on compactness and completeness are proved. Arithmetical theories based on J. Lukasewicz's logic and on its constructive (intuitionistic) variant are investigated; the theorem on effective Luk-incompleteness for a large class of arithmetical systems is proved which is a three-valued analogue of K. Goedel's famous theorem on the incompleteness of formal theories. Three-valued analogues of M. Presburger's arithmetical system are defined; it is proved that they are Luk-complete but not complete in the classical sense.
Received: 20.12.2002
Citation:
I. D. Zaslavsky, “Formal axiomatic theories on the base of three-valued logic”, Computational complexity theory. Part VIII, Zap. Nauchn. Sem. POMI, 304, POMI, St. Petersburg, 2003, 19–74; J. Math. Sci. (N. Y.), 130:2 (2005), 4578–4597
Linking options:
https://www.mathnet.ru/eng/znsl877 https://www.mathnet.ru/eng/znsl/v304/p19
|
Statistics & downloads: |
Abstract page: | 453 | Full-text PDF : | 172 | References: | 46 |
|