Abstract
It is well known that the familiar Sheffer stroke function of the 2-valued propositional calculus is functionally complete (i.e., for any m, all 22m truth functions of m variables can be defined1 in terms of the stroke function). Indeed, it is not difficult to show that of the 16 2-valued functions of two variables, exactly two of them are functionally complete.
Publisher
Cambridge University Press (CUP)
Reference12 articles.
1. Definition of Post's Generalized Negative and Maximum in Terms of One Binary Operation
2. An Asymptotic Formula for the Number of Complete Propositional Connectives
3. Some analogues of the Sheffer stroke function in n-valued logic;Martin;Indagationes Mathematicae,,1950
4. Some completeness criteria for sets of functions over a finite domain. I, II;Salomaa;Annales Vniversitates Turkuensis,1962
Cited by
15 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献
1. The Zhegalkin Polynomial of Multiseat Sole Sufficient Operator;Modeling and Analysis of Information Systems;2023-06-14
2. Quantifier Free Definability on Infinite Algebras;Proceedings of the 31st Annual ACM/IEEE Symposium on Logic in Computer Science;2016-07-05
3. Zero-place operations and functional completeness, and the definition of new connectives;History and Philosophy of Logic;1993-01
4. On sheffer symmetric functions in three-valued logic;Discrete Applied Mathematics;1988-03
5. Onn-Valued Sheffer Functions;Zeitschrift für Mathematische Logik und Grundlagen der Mathematik;1979