On η-valued functionally complete truth functions

1967 ◽  
Vol 32 (2) ◽  
pp. 190-195 ◽  
Author(s):  
R. L. Graham
Keyword(s):  
Propositional Calculus ◽  
Sheffer Stroke ◽  
Functions Of Two Variables

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.

Questions on Logical Inference

1973 ◽  
Vol 7 ◽  
pp. 30-48
Author(s):  
Rush Rhees
Keyword(s):  
Logical Inference ◽  
Fundamental Notion ◽  
Sheffer Stroke

A fundamental notion of the Tractatus is that of the repetition of an operation. The operation specially mentioned is the simultaneous negation represented by the Sheffer stroke. ‘If an operation is applied repeatedly to its own results, I speak of successive applications of it. … In a similar sense I speak of successive applications of more than one operation to a number of propositions’ (5.2521).

scholarly journals Filters of strong Sheffer stroke non-associative MV-algebras

2021 ◽  
Vol 29 (1) ◽  
pp. 143-164
Author(s):  
Tahsin Oner ◽  
Tugce Katican ◽  
Arsham Borumand Saeid ◽  
Mehmet Terziler
Keyword(s):  
Congruence Relation ◽  
Sheffer Stroke ◽  
Isomorphism Theorems ◽  
Mv Algebras

Abstract In this paper, at first we study strong Sheffer stroke NMV-algebra. For getting more results and some classification, the notions of filters and subalgebras are introduced and studied. Finally, by a congruence relation, we construct a quotient strong Sheffer stroke NMV-algebra and isomorphism theorems are proved.

scholarly journals Interval Sheffer Stroke Basic Algebras and Yang-Baxter Equation

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Tahsin Oner ◽  
Tugce Katican
Keyword(s):  
Algebraic Structure ◽  
Basic Algebra ◽  
Baxter Equation ◽  
Sheffer Stroke

AbstractIn this study, we give basic definitions and notions about Sheffer stroke operation and Sheffer stroke basic algebra. After presenting Sheffer stroke basic algebra on a given interval, named interval Sheffer stroke basic algebra, we give some features of an interval Sheffer stroke basic algebra. Then we investigate solutions to the set-theoretical Yang-Baxter equation in this algebraic structure by using its features.

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