Studia Logica 38 (4):407 - 418 (1979)
In this paper two different formulations of Robinson's arithmetic based on relevant logic are examined. The formulation based on the natural numbers (including zero) is shown to collapse into classical Robinson's arithmetic, whereas the one based on the positive integers (excluding zero) is shown not to similarly collapse. Relations of these two formulations to R. K. Meyer's system R# of relevant Peano arithmetic are examined, and some remarks are made about the role of constant functions (e.g., multiplication by zero) in relevant arithmetic.
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References found in this work BETA
Computability and Logic.George Boolos, John Burgess, Richard P. & C. Jeffrey - 2007 - Cambridge University Press.
Algebraic Completeness Results for R-Mingle and its Extensions.J. Michael Dunn - 1970 - Journal of Symbolic Logic 35 (1):1-13.
Entailment. Vol. 1.Alan Ross Anderson & Nuel D. Belnap - 1977 - Canadian Journal of Philosophy 7 (2):405-411.
A Theorem in 3-Valued Model Theory with Connections to Number Theory, Type Theory, and Relevant Logic.J. Michael Dunn - 1979 - Studia Logica 38 (2):149 - 169.
Citations of this work BETA
Relevant Predication 1: The Formal Theory. [REVIEW]J. Michael Dunn - 1987 - Journal of Philosophical Logic 16 (4):347 - 381.
Conditionals, Quantification, and Strong Mathematical Induction.Daniel H. Cohen - 1991 - Journal of Philosophical Logic 20 (3):315 - 326.
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