A Crash Course in Optimality TheoryOT in General: Robot Ethics OT in Phonology: Final Devoicing...

OT in General: Robot Ethics OT in Phonology: Final Devoicing

A Crash Course in Optimality Theory

Jochen Trommerjtrommer@uni-leipzig.de

University of LeipzigDepartment of Linguistics

Concatenative Approaches toNonconcatenative Morphology

EGG 2008

Jochen Trommer jtrommer@uni-leipzig.de A Crash Course in Optimality Theory

Optimality Theory (in General)

a formalism which allows to choose between alternative options

for a given situation

on the basis of (potentially) contradicting

ranked preferences (constraints)

Optimality Theory (Phonology)

An application of this formalism to Phonology

Substantial assumptions on possible representations and constraints

OT in General: Robot Ethics

Isaac Asimovs ethical rules for the behaviour of robots(the “three laws of robotics:”)

1. A robot may not injure a human being or, throughinaction, allow a human being to come to harm.

2. A robot must obey the orders given it by humanbeings, except where such orders would conflictwith the First Law.

3. A robot must protect its own existence, as long assuch protection does not conflict with the First orSecond Law.

Robot Ethics and Potential Conflicts

1. A robot may not injure a human being or, throughinaction, allow a human being to come to harm.

2. A robot must obey the orders given it by humanbeings, except where such orders wouldconflict with the First Law.

3. A robot must protect its own existence, as long assuch protection does not conflict with the Firstor Second Law.

Robot Ethics in OT

Instead of stipulating in single rules

how they interact with other rules

the rules are formulated as completely general constraints

which are ranked among each other

Robot Ethics in OT

*INJURE HUMAN : A robot may not injure a human being or,through inaction,allow a human being to come to harm.

OBEY ORDER: A robot must obeythe orders of human beings.

PROTECT EXISTENCE: A robot must protect its own existence.

Ranking:

*INJURE HUMAN: � OBEY ORDER � PROTECT EXISTENCE

Story A:

Human says to Robot: Kill my wife!

1. R kills H’s wife2. R kills H (who gave him the order)3. R doesn’t kill anyone4. R kills himself

Evaluating Possible Outcomes

1. Setting up a tableau

2. Assigning violation marks

3. Eliminating suboptimal candidates

Step 1: Setting up a Tableau for Story A

Input: H says to R: Kill my wife!*INJURE OBEY PROTECT

HUMAN ORDER EXISTENCE

R kills H’s wifeR kills HR doesn’t kill anyoneR kills himself

Step 2: Assigning Violation Marks for Story A

R kills H’s wife *R kills H * *R doesn’t kill anyone *R kills himself * *

Step 3: Eliminating Suboptimal Candidates for Story A

R kills H’s wife *!R kills H *! *

+ R doesn’t kill anyone *R kills himself * *!

Optimality Theory: Evaluation of Tableaus

for the constraints x ∈ 1 . . . n

I remove all candidats from the candidate set, which aresuboptimal for constraint x

until there is only 1 candidate left

Optimality Theory: Evaluation of Tableaus

I Remove all candidates from the candidate set which aresuboptimal for constraint 1If there is only 1 candidate left: Stop!

I . . .

Optimality Theory: Symbols

* Star Constraint Violation

! Exclamation Mark (after star) Fatal Constraint Violation

+ Pointing Hand Optimal candidate

Shading Irrelevant Tableau Cells

Ranking Matters: A Different Ranking for Story A

Input: H says to R: Kill my wife!OBEY *INJURE PROTECT

+ R kills H’s wife *R kills H *! *R doesn’t kill anyone *!R kills himself *! *

Input Matters: Story B

Input: H says to Robot: Kill my wife or I kill her!*INJURE OBEY PROTECT

+ R kills H’s wife *R kills H * *!R doesn’t kill anyone * *!R kills himself * *! *

Optimality Theory in Phonology

Inputs: Phonological representations from Lexicon + Morphology

Outputs: Modified phonological forms

Final devoicing in German

Rat [öa:t] ‘advice’ Rat+es [öa:t+@s] ‘advice (gen.)’

Stück [Styk] ‘piece’ Stück+es [Styk+@s] ‘piece’ (gen.)

Rad [öa:t] ‘wheel’ Rades [öa:d+@s] ‘wheel’ (gen.)

Tag [ta:k] ‘day’ Tages [ta:g+@s] ‘day’ (gen.)

Voiced stops get voiceless at the end of a word

Final devoicing in Rule-based Phonology

[+voiced] Ô [–voiced] / #

/öa:d/ ⇒ /öa:t/

Final Devoicing in Optimality Theory

Input: tu:gend+ a. tu:gent

b. du:gentc. tu:gendd. du:gend

The Basic Conflict in Optimality Theory

Markedness Constraints: Make things better!

Treue-Beschränkungen: Don’t change!

Constraints

*[+voiced]# Stops at the word endshould not be [+voiced]

IDENT [voiced] Corresponding input and output soundsshould have identical valuesfor the feature [voiced]

Markedness

Faithfulness

The Interpretation of OT-Constraints

In the literature, OT-Constraints are oftenformulated as positive requirements,

but technically every constraint is a functionwhich assigns a specific number of constraint violationsfor a specific input-output pair

*[+voiced]#

Input: tu:gend *[+voiced]#+ a. tu:gent+ b. du:gent

c. tu:gend *!d. du:gend *!

*[+voiced]# Stops at the word endshould not be [+voiced]Count 1 constraint violationfor every voiced stop at the end of a word

IDENT [voiced]

Input: tu:gend IDENT [voiced]a. tu:gent *!b. du:gent *!*

+ c. tu:gendd. du:gend *!

IDENT [voiced] Corresponding input and output soundsshould have identical valuesfor the feature [voiced]Count 1 constraint violation for every output soundwhich has a different value of [voiced]with respect to the corresponding input sound

Final Devoicing in Optimality Theory: Ranking

Input: tu:gend *[+voiced]# IDENT [voiced]+ a. tu:gent *

b. du:gent **!c. tu:gend *!d. du:gend *! *

Final Devoicing in Optimality Theory: Ranking

Input: tu:gend *[+voiced]# IDENT [voiced]+ a. tu:gent *

b. du:gent **!c. tu:gend *!d. du:gend *! *

Optimality-theoretic Constraints . . .

I are universal (innate?)

I phonetically grounded

I freely rankable

Different rankings resultin the grammars of different languages

Final devoicing . . .

I is attested in many unrelated languages

I doesn’t have to be learned (Stampe, 1973)

I occurs also in the acquisition of languages without finaldevoicing (Smith, 1973)

Ranking for Languages without Final devoicing

Input: tu:gend IDENT [voiced] *[+voiced]#a. tu:gent *!b. du:gent *!*

+ c. tu:gend *d. du:gend *! *

A Crash Course in Optimality TheoryOT in General: Robot Ethics OT in Phonology: Final Devoicing...

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