  We propose a framework to model an operational conversational negation by
applying worldly context (prior knowledge) to logical negation in compositional
distributional semantics. Given a word, our framework can create its negation
that is similar to how humans perceive negation. The framework corrects logical
negation to weight meanings closer in the entailment hierarchy more than
meanings further apart. The proposed framework is flexible to accommodate
different choices of logical negations, compositions, and worldly context
generation. In particular, we propose and motivate a new logical negation using
matrix inverse.
  We validate the sensibility of our conversational negation framework by
performing experiments, leveraging density matrices to encode graded entailment
information. We conclude that the combination of subtraction negation and
phaser in the basis of the negated word yields the highest Pearson correlation
of 0.635 with human ratings.
