Full Idea
A theory is 'negation complete' if it decides every sentence of its language (either the sentence, or its negation).
Gist of Idea
A theory is 'negation complete' if it proves all sentences or their negation
Source
Peter Smith (Intro to Gödel's Theorems [2007], 03.4)
Book Reference
Smith,Peter: 'An Introduction to Gödel's Theorems' [CUP 2007], p.24