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Josefina Sierra Josefina Santibez

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Title: Josefina Sierra Josefina Santibez

1
Acquisition of Linguistic Competencefor
Communicating Propositional Logic Sentences

Josefina Sierra Josefina
Santibáñez
Tech. Univ of Cataluña University of
La Rioja
Spain
Spain

Language Game Guessing (Steels 1999)
Speaker chooses a formula from a propositional
language, generates a sentence for expressing the
formula and communicates the sentence to hearer.
Hearer tries to interpret the sentence generated
by the speaker. If it can parse it using its
lexicon and grammar, it extracts a meaning.
Success speakers formula ? hearers
meaning
If not success, the speaker communicates the
formula it had in mind to hearer. They adjust
their grammars to become sucessful in future.

Goals of the Experiments
Observe the evolution of
The communicative success average of sucess-ful
language games in the last ten games played by
the agents.
The internal grammars constructed by the
individual agents.
The external language used by the population.

Definite clause grammarsemantic, score, use
s(right, 0.25, 20) ? right
s(light, 0.70, 50) ? light
s(P,Q, S, 12) ? 1, c1(P,S1,C1), s(Q,S2,C2), S
is S1?S2?0.01
c1(not, 0.80, 55) ? not
s(P,Q,R,S,3) ? 2, c2(P,S1,C1), s(Q,S2,C2), s(R,
S3,C3), S is S1?S2?S3?0.01
c2(and, 0.50, 35) ? and
Formula Meaning
Sentence
right ? light and, right, light
rightandlight
light not, light
notlight

Invention
Generates a sentence E for a meaning M
If M is atomic, it invents a new word E.
If M is a list, it tries to construct an
expression for each of the elements in M using
the agents grammar.
If it cannot construct an expression for an
element using its grammar, it invents a new
expression.
It concatenates the expressions associated with
the elements of M randomly in order to construct
a sen-tence E for the whole meaning M.
Adds a new rule to the grammar s(M, 0.01, 0) ?
E

Adoption
Communication fails because
The hearer cannot parse the speakers sentence
The speaker communicates the formula it had in
mind to the hearer.
The hearer adopts an association between that
formula and the sentence used by the speaker.
s(M, 0.01, 0) ? E
The hearer can parse the sentence, but its
interpre-tation is not consistent with the
speakers meaning.
Hearer and speaker decrase the scores of used
associations.
It may adopt an association between the formula
and the sentence used by the speaker.

Induction
The agents use some induction mechanisms to
extract
generalisations from the grammar rules learnt
so far.
The induction rules used in the experiments are
based
on the following rules proposed in (Kirby
2002)
Simplification
Chunk
They are applied whenever the agents invent or
adopt
a new association.

Simplification
r1 ? left(m1, S1) ? e1 , S1 is E?s1
r2 ? n(m1, S2) ? e1, S2 is s2
Rule r1 is replaced with the following rule
left(X, S1) ? n(X,S), S1 is E?S?0.01
where
X and S are new variables,
s1 and s2 are the scores of rules r1 and r2, and
E is the product of the score variables of the
arith-metic expression on the right hand side of
rule r1.

Simplification example 1
r1 ? s(right, S1) ? right, S1 is 0.25
r2 ? s(and,light,right, S2) ? andlightright,
S2 is 0.10
Rule r2 is replaced with rule r3
r3 ? S(and,light,R, S) ? andlight, s(R, S3), S
is S3 ? 0.01
r4 ? s(light, S4) ? light, S4 is 0.70
Rule r3 is replaced with rule r5
r5 ? s(and,Q,R, S) ? 1, and, s(Q, S2), s(R,
S3), S is S3 ? S2 ? 0.01

Simplification example 2
r1 ? s(right, S1) ? right, S1 is 0.25
r6 ? s(or,light,right, S6) ? orlightright,
S6 is 0.1
Rule r6 is replaced with rule r7
r7 ? S(or,light,R, S) ? orlight, s(R, S3), S
is S3?0.01
r4 ? s(light, S4) ? light, S4 is 0.70
Rule r7 is replaced with rule r8
r8 ? s(or,Q,R, S) ? 1, or, s(Q, S2), s(R, S3),
S is S2?S3?0.01

Simplification example 3
r1 ? s(right, S1) ? right, S1 is 0.25
r9 ? s(or,light,right, S9) ? lightorright, S9
is 0.10
Rule r9 is replaced with rule r10
r10 ? S(or,light,R, S) ? lightor, s(R, S3), S
is S3?0.01
r4 ? s(light, S4) ? light, S4 is 0.70
Rule r10 is replaced with rule r11
r11 ? s(or,Q,R, S) ? 2, or, s(Q, S2), s(R, S3),
S is S2?S3?0.01

Chunk I
r1 ? left(f(m1), S1) ? right(e1)?, S1 is E?s1
r2 ? left(f(m2), S2) ? right(e2)?, S1 is E?s1
A new category symbol n is created and rules
added
n(m1, 0.01) ? e1 n(m2, 0.01) ?
e2
Rules r1 and r2 are replaced with rule r3, of the
form
left(f(X), S3) ? right?(n(X, S)), S3 is
E?S?0.01
where
X and S are new variables,
s1 and s2 are the scores of rules r1 and r2, and
E is the product of the score variables of the
arith-metic expression on the right hand side of
rule r1.

Chunk I example 1
r1 ? s(and,Q,R, S) ? 1, and, s(Q, S2), s(R,
S3), S is S2?S3?0.10
r2 ? s(or,Q,R, S) ? 1, or, s(Q, S2), s(R, S3),
S is S2?S3?0.30
The following new rules are added to grammar
c2(and, 0.01) ? and c2(or, 0.01) ? or
Rules r1 and r2 are replaced with rule r3
r3 ? s(P,Q,R, S) ? 1, c2(P, S1), s(Q, S2),
s(R, S3), S is S1?S2?S3?0.01

Chunk I example 2
r1 ? s(and,Q,R, S) ? 1, and, s(Q, S2), s(R,
S3), S is S2?S3?0.10
r2 ? s(or,Q,R, S) ? 2, or, s(Q, S2), s(R, S3),
S is S2?S3?0.30
Chunk cannot be applied to r1 and r2, because
they
place the expressions associated with the
connectives
and and or in different positions in the
sentence.

Chunk I example 3
r1 ? s(and,Q,R) ? 2, and, s(R, S3), s(Q, S2),
S is S2?S3?0.10
r2 ? s(or,Q,R, S) ? 2, or, s(Q, S2), s(R, S3),
S is S2?S3?0.30
Chunk cannot be applied to r1 and r2, because
they
place the expressions associated with the
arguments
of the binay connective, Q and R, in different
posi-
tions in the sentence.
Rules must agree on the positions of the expres-
sions associated with the connectives and their
arguments in the sentence.

Chunk II
r1 ? left(f(X), S1) ? right?(n(X, S)),
r2 ? left(f(m1), S2) ? right?(e1),
Rule r2 is replaced with the following rule
n(m1, 0.01) ? e1
right?(X) is the result of removing the
arithmetic ex-
pression of the right hand side of a grammr rule.

Chunk II example 1
r1 ? s(P,Q,R, S) ? 1, c2(P, S1), s(Q, S2), s(R,
S3), S is S1?S2?S3?0.20
r2 ? s(iff,Q,R, S) ? 1, iff, s(Q, S2), s(R,
S3), S is S2?S3?0.50
Rule r2 is replaced with the following rule
c2(iff, 0.01) ? iff

Chunk II example 2
r1 ? s(P,Q,R, S) ? 1, c2(P, S1), s(Q, S2), s(R,
S3), S is S1?S2?S3?0.20
r2 ? s(iff,Q,R, S) ? 3, iff, s(Q, S2), s(R,
S3), S is S2?S3?0.50
Chunk cannot be applied, because rule r1 places
the
expresion associated with the connective in first
po-
sition in the sentence and rule r2 places the
expres-
sion associated with the connective third
position.

Need for Coordination The agents must reach
agreements on how to
name propositional constants and connectives
a1 if ? if
a2 if ? si
order the expressions associated with the
different components of non-atomic meanings
consistently
a1 not ? un, 2pos not, right ?
rightnot
a2 not ? un, 1pos not, right ?
notright
a1 if ? bin, 2pos, inv if,right,light ?
lightifright
a2 if ? bin, 2pos, noinv if,right,light ?
rightiflight

Self-organization Coordinate agents grammars
The agents construct a shared external language
and
prefer using the rules in that language over the
rest
in the rules in their individual grammars.
The scores of the rules indicate the agents
preferences
meaning ? sentence1 highest score
competing sentences sentence2, ,
sentenceN
sentence ? meaning1 highest score
competing meanings meaning2, ,
meaningN
The score of a sentence (or meaning) is computed
at
generation (parsing) multiplying the scores of
the rules
involved (Vogt 2005).

Score of a sentence (meaning) example
r1 s(right, 0.25) ? right r2 c1(if,
0.50) ? if
r3 s(light, 0.70) ? light r4 c2(if,
0.10) ? si
r5 s(P,Q,R,S) ? 1, c1(P,S1), s(Q,S2), s(R,S3),
S is S1?S2?S3?0.10
r6 s(P,Q,R,S) ? 1, c2(P,S1), s(R,S3), s(Q,S2),
S is S1?S2?S3?0.01
Meaning if, right, light ? Generation
Sentence ifrightlight score
0.50?0.25?0.70?0.10
Comp senten silightright score
0.10?0.25?0.70?0.01

Coordination takes place at the third stage of a
lan-guage game when the speaker communicates the
meaning it had in mind to the hearer.
hearers meaning ? speakers meaning
Speaker increases scores of rules ? sentence
decreases scores of rules ? competing
sentences
Hearer increases scores of rules ? meaning
decreases scores of rules ? competing
meanings
hearers meaning ? speakers meaning
Speaker and hearer decrease scores of rules they
used for generating and interpreting the sentence.

Reinforcement and Inhibition
The rules used successfully are reinforced.
The rules used for generating competing sentences
or competing meanings are inhibited.
The rules used for updating scores of grammar
rules (Steels 1999) replace the original score S
with
S1 ? minimum(1, S 0.1) if the score is
increased
S2 ? maximum(0, S ? 0.1) if the score is
decreased
Purging the rules that have been used more than
30 times and have scores ? 0.01 are removed from
the agents grammars.

24
Experiments Evolution Communicative Success
guessing game 5 agents, 15000 games about
propositional formulas La, b, c, r, l, u
constructed using ?, ?, ?, ?, ?
25
Guessing negation ?
26
Guessing conjuction ? (commut)
27
Guessing implication ? (non-com)

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