Strengths of negation

This file defines the strengths of negation a context can carry, Zwarts's hierarchy of weak, anti-additive and anti-morphic contexts, which are van der Wouden's minimal, regular and classical negation. A context is weakly negative when it is downward entailing, anti-additive when it also turns disjunctions into conjunctions, and anti-morphic when it also turns conjunctions into disjunctions, as clausal negation does. Each strength is the function class of a natural-logic signature, and the strength a signature realizes is the greatest strength whose class contains it, so that the strengths sit among the signatures as a chain in reverse.

References

• Zwarts 1998, Three Types of Polarity
• van der Wouden 1997, Negative Contexts: Collocation, Polarity and Multiple Negation formalized
• Icard 2012, Inclusion and Exclusion in Natural Language formalized
• Ladusaw 1979, Polarity Sensitivity as Inherent Scope Relations formalized