David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
History and Philosophy of Logic 23 (3):215--36 (2002)
We show that classical two-valued logic is included in weak extensions of normal three-valued logics and also that normal three-valued logics are best viewed not as deviant logics but instead as strong extensions of classical two-valued logic obtained by adding a modal operator and the right axioms. This article develops a general method for formulating the right axioms to construct a two-valued system with theorems that correspond to all of the logical truths of any normal three-valued logic. The extended classical system can then express anything that can be expressed in the three-valued logic, so there can be no reason to abandon two-valued logic in favor of three-valued logic. Moreover, the two-valued modal system is preferable, because it enables us to study interactions of different operators with different rationales. It also makes it easier to introduce quantifiers and iteration. Nothing is lost and much is gained by choosing the extended two-valued approach over normal three-valued logics
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
No references found.
Citations of this work BETA
No citations found.
Similar books and articles
E. H. Alves & J. A. D. Guerzoni (1990). Extending Montague's System: A Three Valued Intensional Logic. Studia Logica 49 (1):127 - 132.
Helena Rasiowa (1979). Algorithmic Logic. Multiple-Valued Extensions. Studia Logica 38 (4):317 - 335.
Grzegorz Malinowski (1993). Many-Valued Logics. Oxford University Press.
A. Avron & B. Konikowska (2008). Rough Sets and 3-Valued Logics. Studia Logica 90 (1):69 - 92.
Richard DeWitt (2005). On Retaining Classical Truths and Classical Deducibility in Many-Valued and Fuzzy Logics. Journal of Philosophical Logic 34 (5/6):545 - 560.
A. S. Karpenko (1983). Factor Semantics Forn-Valued Logics. Studia Logica 42 (2-3):179 - 185.
Added to index2009-08-21
Total downloads13 ( #113,877 of 1,096,425 )
Recent downloads (6 months)2 ( #134,922 of 1,096,425 )
How can I increase my downloads?