Notes on computational linguistics.pdf - UCLA Department of ...

Stabler - Lx 185/209 2003
15.2 Monotonicity inference: A more general and concise formulation
Adapted from (Fyodorov, Winter, and Francez, 2003; Bernardi, 2002; Sanchez-Valencia, 1991; Purdy, 1991).
1. Label the derivation (i.e. the lexical sequence) as follows:
i. bracket all merged pairs
ii. label all quantifiers with their monotonicities in the standard way:
iii. for ◦, ⋄ in {↑, ↓, ˜}, label(◦Q⋄ A) as (◦Q⋄ A ◦ )
e.g. ↓every↑, ↑some↑, ↓no↓, ↑not-all↓, ˜most↑, ˜exactly 5˜
(↓every↑ student ↓ )
iv. for ◦, ⋄ in {↑, ↓, ˜}, label(P(◦Q⋄ A ◦ ) as (P ⋄ (◦Q⋄ A ◦ )
(sing ↑ (↓every↑ student ↓ ))
(praise ↑ (↓every↑ student ↓ ))
((praise ↑ (↓every↑ student ↓ ) ↑ (↑some↑ teacher ↑ )))
v. label outermost parentheses ↑ (or if no parentheses at all, label single element ↑)
2. Each constituent A has the superscripts of the constituents containing it and its own.
Letting ↑= 1, ↓= −1, ˜ = 0, the polarity of A is the polarity p=the product of its superscripts.
3. Then for any expression with constitutent A with non-zero polarity p, wehavetherulemon:
(...A...) A≤ p B
(...B...)
That is, you can increase any positive constituent, and decrease any negative one.
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