scholarly journals On the learnability of disjunctive normal form formulas

1995 ◽  
Vol 19 (3) ◽  
pp. 183-208 ◽  
Author(s):  
Howard Aizenstein ◽  
Leonard Pitt
Keyword(s):  
Normal Form ◽  
Disjunctive Normal Form

On closure under direct product

1958 ◽  
Vol 23 (2) ◽  
pp. 149-154 ◽  
Author(s):  
C. C. Chang ◽  
Anne C. Morel
Keyword(s):  
Normal Form ◽  
Direct Product ◽  
Disjunctive Normal Form ◽  
Negative Answer ◽  
Sufficient Condition ◽  
Natural Question ◽  
Existential Quantifier ◽  
Relational Systems ◽  
Image Position

In 1951, Horn obtained a sufficient condition for an arithmetical class to be closed under direct product. A natural question which arose was whether Horn's condition is also necessary. We obtain a negative answer to that question.We shall discuss relational systems of the formwhere A and R are non-empty sets; each element of R is an ordered triple 〈a, b, c〉, with a, b, c ∈ A.1 If the triple 〈a, b, c〉 belongs to the relation R, we write R(a, b, c); if 〈a, b, c〉 ∉ R, we write (a, b, c). If x0, x1 and x2 are variables, then R(x0, x1, x2) and x0 = x1 are predicates. The expressions (x0, x1, x2) and x0 ≠ x1 will be referred to as negations of predicates.We speak of α1, …, αn as terms of the disjunction α1 ∨ … ∨ αn and as factors of the conjunction α1 ∧ … ∧ αn. A sentence (open, closed or neither) of the formwhere each Qi (if there be any) is either the universal or the existential quantifier and each αi, l is either a predicate or a negation of a predicate, is said to be in prenex disjunctive normal form.

Privacy-preserving disjunctive normal form operations on distributed sets

2013 ◽  
Vol 231 ◽  
pp. 113-122 ◽  
Author(s):  
Ji Young Chun ◽  
Dowon Hong ◽  
Ik Rae Jeong ◽  
Dong Hoon Lee
Keyword(s):  
Normal Form ◽  
Disjunctive Normal Form ◽  
Privacy Preserving
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