David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
In classical and intuitionistic arithmetics, any formula implies a true equation, and a false equation implies anything. In weaker logics fewer implications hold. In this paper we rehearse known results about the relevant arithmetic R, and we show that in linear arithmetic LL by contrast false equations never imply true ones. As a result, linear arithmetic is desecsed. A formula A which entails 0 = 0 is a secondary equation; one entailed by 0 6= 0 is a secondary unequation. A system of formal arithmetic is secsed if every extensional formula is either a secondary equation or a secondary unequation. We are indebted to the program MaGIC for the simple countermodel SZ7, on which 0 = 1 is not a secondary formula. This is a small but signi cant success for automated reasoning.
|Keywords||No keywords specified (fix it)|
No categories specified
(categorize this paper)
|Through your library||Only published papers are available at libraries|
Similar books and articles
John R. Lucas (1961). Minds, Machines and Godel. Philosophy 36 (April-July):112-127.
Emma Smith (2008). Pitfalls and Promises: The Use of Secondary Data Analysis in Educational Research. British Journal of Educational Studies 56 (3):323 - 339.
Robert K. Meyer (1998). ⊃E is Admissible in “True” Relevant Arithmetic. Journal of Philosophical Logic 27 (4):327 - 351.
Agustín Rayo (2002). Frege's Unofficial Arithmetic. Journal of Symbolic Logic 67 (4):1623-1638.
M. Krynicki & K. Zdanowski (2005). Theories of Arithmetics in Finite Models. Journal of Symbolic Logic 70 (1):1-28.
Zlatan Damnjanovic (1995). Minimal Realizability of Intuitionistic Arithmetic and Elementary Analysis. Journal of Symbolic Logic 60 (4):1208-1241.
Claudio Bernardi (1976). The Uniqueness of the Fixed-Point in Every Diagonalizable Algebra. Studia Logica 35 (4):335 - 343.
Robert K. Meyer (1998). ÂE is Admissible in ÂTrueâ Relevant Arithmetic. Journal of Philosophical Logic 27 (4):327-351.
M. D. G. Swaen (1991). The Logic of First Order Intuitionistic Type Theory with Weak Sigma- Elimination. Journal of Symbolic Logic 56 (2):467-483.
Michael Potter (1998). Classical Arithmetic as Part of Intuitionistic Arithmetic. Grazer Philosophische Studien 55:127-41.
Added to index2010-12-22
Total downloads6 ( #160,476 of 1,013,596 )
Recent downloads (6 months)1 ( #64,884 of 1,013,596 )
How can I increase my downloads?