Independent Axioms for Infinite-Valued Logic
- 1 September 1963
- journal article
- Published by Cambridge University Press (CUP) in The Journal of Symbolic Logic
- Vol. 28 (3) , 217-221
- https://doi.org/10.2307/2271067
Abstract
Recent interest in Łukasiewicz' Lℵ0, raises the question whether this axiomatic system can be simplified [2]. It is known that Łukasiewicz' fourth axiom CCCPQCQPCQP is dependent [4] p. 51. The axiomatic system resulting from deleting the fourth axiom from Lℵ0 will be shown to be “minimal” in the sense that the axioms and rules of inference are mutually independent; consequently, no further simplification of Lℵ0, is possible. By switching basic operators, however, simplified modifications of Lℵ0, can be constructed.Keywords
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- Many-valued Logics. By J.B. Rosser and A.R. Turquette. Pp. 124. F1. 12. 1952. Studies in logic and the foundations of mathematics. (North-Holland Publishing Co., Amsterdam)The Mathematical Gazette, 1953
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