Transcript The Harmonic Mind - Cognitive Science at Johns Hopkins

Learnability in OT
• Learning algorithm
– Provably correct and efficient (under strong
assumptions)
– Sources:
• Tesar ‘95 et seq.
• Tesar & Smolensky ‘93, …, ‘00
• Also: Boersma ’98 et seq.
– If you hear A when you expected to hear E,
minimally demote each constraint violated by
A below a constraint violated by E
May 7, 2003
1
University of Amsterdam
Constraint Demotion Learning
• If you hear A when you expected to hear E,
minimally demote each constraint violated
by A below a constraint violated by E
Correctly handles difficult case: multiple violations in E
in +
Candidates
possible
☹☞E
May 7, 2003
☺
☞
FAITH
*
inpossible
A impossible
2
MARK
FAITH
(NPA)
*
*
University of Amsterdam
Initial State in OT
• M ≫ F is learnable with
/in+possible/→impossible
– ‘not’ = in- except when followed by …
– “exception that proves the rule”: M = NPA
• M ≫ F is not learnable from data if there are
no ‘exceptions’ (alternations) of this sort, e.g.,
if no affixes and all underlying morphemes
have mp: √M and √F, no M vs. F conflict, no
evidence for their ranking
• Thus must have M ≫ F in the initial state, ℌ0
May 7, 2003
3
University of Amsterdam