Hostname: page-component-848d4c4894-75dct Total loading time: 0 Render date: 2024-05-21T17:29:58.696Z Has data issue: false hasContentIssue false
  • English
  • Français

Independent Axioms for Infinite-Valued Logic1

Published online by Cambridge University Press:  12 March 2014

Atwell R. Turquette
Atwell R. Turquette*
Affiliation:
University of Illinois
Get access Rights & Permissions [Opens in a new window]

Extract

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.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 28 , Issue 3 , September 1963 , pp. 217 - 221
Copyright
Copyright © Association for Symbolic Logic 1964

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

1

Portions of this paper were presented at the meeting of the International Congress of Mathematicians, August 1962, Stockholm, Sweden.

References

[1]Łukasiewicz, Jan, A system of modal logic, The journal of computing systems, vol. 1 no. 3 (1953), pp. 111–149.Google Scholar
[2] Alan Rose and Rosser, J. B., Fragments of many-valued statement calculi, Transactions of the American Mathematical Society, vol. 87 (1958), pp. 1–53.Google Scholar
[3]Rosser, J. B. and Turquette, A. R., Many-valued logics, Amsterdam (North Holland), 1952.Google Scholar
[4]Tarski, Alfred, Logic, semantics, metamathematics, translated by Woodger, J. H., Oxford (Clarendon), 1956.Google Scholar