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On Partial Classes Containig All Monotone and Zero‐Preserving Total Boolean Functions
Author(s) -
Strauch Birger
Publication year - 1997
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.19970430407
Subject(s) - mathematics , partial function , monotone polygon , boolean function , class (philosophy) , discrete mathematics , boolean expression , complete boolean algebra , zero (linguistics) , set (abstract data type) , two element boolean algebra , combinatorics , pure mathematics , algebra over a field , computer science , linguistics , philosophy , geometry , artificial intelligence , programming language , filtered algebra
We describe sets of partial Boolean functions being closed under the operations of superposition. For any class A of total functions we define the set ( A ) consisting of all partial classes which contain precisely the functions of A as total functions. The cardinalities of such sets ( A ) can be finite or infinite. We state some general results on ( A ). In particular, we describe all 30 closed sets of partial Boolean functions which contain all monotone and zero‐preserving total Boolean functions.