An approach to glivenko's theorem in algebraizable logics
Studia Logica 88 (3) (2008)
| Abstract | In a classical paper [15] V. Glivenko showed that a proposition is classically demonstrable if and only if its double negation is intuitionistically demonstrable. This result has an algebraic formulation: the double negation is a homomorphism from each Heyting algebra onto the Boolean algebra of its regular elements. Versions of both the logical and algebraic formulations of Glivenko’s theorem, adapted to other systems of logics and to algebras not necessarily related to logic can be found in the literature (see [2, 9, 8, 14] and [13, 7, 14]). The aim of this paper is to offer a general frame for studying both logical and algebraic generalizations of Glivenko’s theorem. We give abstract formulations for quasivarieties of algebras and for equivalential and algebraizable deductive systems and both formulations are compared when the quasivariety and the deductive system are related. We also analyse Glivenko’s theorem for compatible expansions of both cases. | |||||||||
| Keywords | No keywords specified (fix it) | |||||||||
| Categories | ||||||||||
| Options |
|
|||||||||
Download options| PhilPapers Archive |
Upload a copy of this paper Check publisher's policy on self-archival Papers currently archived: 5,653 |
| External links |
 |
| Through your library | Configure |
Similar books and articlesJosep Maria Font, Ramon Jansana & Don Pigozzi (2006). On the Closure Properties of the Class of Full G-Models of a Deductive System. Studia Logica 83 (1-3):215 - 278.
R. A. Lewin, I. F. Mikenberg & M. G. Schwarze (2000). Algebras and Matrices for Annotated Logics. Studia Logica 65 (1):137-153.
Alexej P. Pynko (1995). Algebraic Study of Sette's Maximal Paraconsistent Logic. Studia Logica 54 (1):89 - 128.
W. J. Blok & J. Rebagliato (2003). Algebraic Semantics for Deductive Systems. Studia Logica 74 (1-2):153 - 180.
Burghard Herrmann (1996). Equivalential and Algebraizable Logics. Studia Logica 57 (2-3):419 - 436.
Burghard Herrmann (1997). Characterizing Equivalential and Algebraizable Logics by the Leibniz Operator. Studia Logica 58 (2):305-323.
Roberto Cignoli & Antoni Torrens Torrell (2006). Free Algebras in Varieties of Glivenko MTL-Algebras Satisfying the Equation 2(X2) = (2x). Studia Logica 83 (1-3):157 - 181.
Guram Bezhanishvili (2001). Glivenko Type Theorems for Intuitionistic Modal Logics. Studia Logica 67 (1):89-109.
Nikolaos Galatos & Hiroakira Ono (2006). Glivenko Theorems for Substructural Logics Over FL. Journal of Symbolic Logic 71 (4):1353 - 1384.
Antoni Torrens Torrell (2008). An Approach to Glivenko's Theorem in Algebraizable Logics. Studia Logica 88 (3):349 - 383.
Analytics
Monthly downloads |
Added to index2009-01-28Total downloads5 ( #160,204 of 548,984 )Recent downloads (6 months)0How can I increase my downloads? |
My notes
Discussion
