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A Tale of Recursion

(A very preliminary version)

ARAVIND K. JOSHIApril 19 2006 (revised May 8 2006)

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Hauser, M.D., Chomsky, N., and Fitch, W.T. 2002 The Facultyof Language: What is it, Who Has It, and How did it evolve?Science 298 pp. 1569-1579

“FLN (faculty of language in the narrow sense) includesrecursion and is the only uniquely human componentof the faculty of language.” –from the Abstract, p.1569

Recursion as the unique property of the faculty of language

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Is recursion the only unique property of the human language faculty?

• There may be some other properties unique to the human language faculty• Here is a candidate: Every construction in a language has variants, i.e., what is said by using a construction can be said in another way (or other ways) preserving semantics. Thus these variants are syntactic variants.

(There will be some frozen expressions which may not have any variants. However, these constructions will not participate in recursion so we can leave them out from our consideration.)

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We will show (by some examples)that the twoproperties mentioned before interact in thefollowing way:A construction may be unboundedly recursivein one or more of its variants but it is not unboundedly recursive in all its variants

We will call this property non-uniformity of recursionThus our claim will be that language has recursion but it is non-uniform

Thus recursion is indirectly bounded!

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An alternate perspectives on LTAG:

• Flexible composition

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Flexible Composition

X

Split at x

XX

supertree of at X

subtree of at X

Adjoining as Wrapping

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X

X

X

X

X

wrapped around i.e., the two components and are wrapped around

supertree of at X

subtree of at X

Flexible CompositionAdjoining as Wrapping

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S

V NP

likes

NP(wh)

e

S

VP

S

NP

V S*

think

VP

substitution

adjoining

Flexible CompositionWrapping as substitutions and adjunctions

NP

- We can also view this composition as wrapped around - Flexible composition

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S*

V NP

likes

NP(wh)

e

S

VP

S

NP

V S*

think

VP

substitution

adjoining

Flexible CompositionWrapping as substitutions and adjunctions

NP

S

and are the two components ofattached (adjoined) to the root node S of attached (substituted) at the foot node S of

Leads to multi-component TAG (MC-TAG)

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Multi-component LTAG (MC-LTAG)

• The two components are used together in one composition step. Both components attach to nodes in an elementary tree.• This preserves locality. Tree local MC-LTAG

• The representation can be used for both -- predicate-argument relationships -- non-p/a information such as scope, focus, etc.

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Tree-local Multi-component LTAG (MC-LTAG)

- Tree-local MC-LTAG- Flexible composition

- Tree-local MC-LTAGs are weakly equivalent (?) - However, Tree-local MC-LTAGs provide structural descriptions not obtainable by LTAGs- Increased strong generative power- In the linguistic context there are always constraints among the components (usually two components), constraints such as domination, immediate domination, c-command, co-indexing, etc. These are structural (linguistic) constraints and not processing constraints

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(1) The gardener who the woman kept calling all day finally came.

(1’) The gardener finally came who the woman kept calling all day.

(2) The gardener who the woman who had lost her keys kept calling all day finally came.

*(2’) The gardener who the woman kept calling all day finally came who had lost her keys.

Extraposition from NP: An example

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NP VP

The gardener finally came

S

NP VP

The gardener finally came

S

S

S who the woman kept calling all day

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NP VP

finally came

S

NP VP

The gardener finally came

S

S

S who the woman kept calling all day

b1: { b11 b12}NP S

NP* S(i) S* S(i)

e

who the woman kept calling all day

ID

The gardener

NP

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NP VP

S

S

S (i) who had lost her keys

NP SThe gardener who the woman (i) kept calling all day

finally came

*

• Recursion of NP extraposition is constrained (Example 1)• Even if it is allowed the result is associated with the semantics of stacked relatives, thus semantically incoherent

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Uniform (U) and non-uniform (NU) recursion

• Recursion is uniform (U) if a recursive construction is semantically coherent in all its variants, i.e., all the “transformed” versions of the construction.• Otherwise it is non-uniform (NU)• Center embedding of relative clauses is NU• Tree-local MC-LTAG can model this non-uniformity of center embedding• Another example: -- Recursive embedding of verbs taking complements– Example 2

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(1)The President will resign today(2) John thinks the President will resign today(3) The President, John thinks, will resign today(4) Mary believes John thinks the President will

resign today*(5) Mary believes the President, John thinks,

will resign today*(6) The President, Mary believes John thinks,

will resign today

Uniform and non-uniform recursion

• This non-uniformity of recursive embedding of verbs taking clausal complements can also be modeled by tree-local MC-LTAG

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Another example – Example 3

(1) Who did Bill invite?(2) Who does John think Bill invited? ? (3) Who did Bill, John thinks, invite?(4) Who does Harry believe John thinks Bill invited??? (5) Who does Harry believe Bill, John thinks, invited??? (6) Who did Bill, Harry believes John, thinks, invite?

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(1) Hans1 Peter2 Marie3 schwimmen3 lassen2 sah1

(2)) P(N1, N2 … Nk) Vk Vk-1 … V1

where P is a permutation of k nouns

Scrambling (Example 4)

• Consider the case where the Ni Vi pairs are purely nested, i.e., (3) N1, N2 … Nk Vk Vk-1 … V1 Clearly, this recursive embedding is uniform (U)• Now regard all other permutations of Ni as variants of (3)• We now have the interesting result …

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Scrambling- Example 4

• Tree-local MC-LTAG can generate all permutations of N’s in (3) (3) N1 N2 … Nk Vk Vk-1 … V1

with correct structural descriptions, i.e., correct semantics for up to 2 levels of embedding (k=3)• Beyond two levels of embedding, not all permutations of N’s can be generated with the correct structural descriptions (semantics) • Recursive embedding of complement clauses is non-uniform, which is modeled by Tree-local MC-TAG

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Scrambling- Example 4

• For k=3, all permutations on N’s are possible

N1 N2 N3 V3 V2 V1N1 N3 N2 V3 V2 V1N2 N1 N3 V3 V2 V1N2 N3 N1 V3 V2 V1N3 N1 N2 V3 V2 V1N3 N2 N1 V3 V2 V1

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• Some elementary trees (possibly multi-component) for a verb with a scrambled argument

VP

Ni VP*

VP

VPNi

Ve

VP*

VP

Ni VP

VP

VPNi

Ve

VP*

VP

Ni VP

VP

VPNi

Ve

b1:b2:b3:

b31:

b32:

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N1 N2 N3 V3 V2 V1

VP

N3 VP

VP

VPN3

eV3

VP

N2 VP

VP

VPN2

V2e

VP*

VP

N1 VP

VP

VPN1

V1e

VP*

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N2 N3 N1 V3 V2 V1

VP

N3 VP*

VP

VPN3

eV3

VP

N2 VP

VP

VPN2

V2e

VP*

VP

N1 VP*

VP

VPN1

V1e

VP*

Now how does the top level subordinator compose?

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N2 N3 N1 V3 V2 V1

VP

N3 VP*

VP

VPN3

eV3

VP

N2 VP

VP

VPN2

V2e

VP*

VP

NP VP*

VP

VPN1

V1e

VP*

VP

XP VP*

VP*

a a1 a2 a3

a3 composes with a2, a1 with a and then the result with a2

( top level subordinator)

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Scrambling- Example 4 For k=4

N1 N2 N3 N4 V4 V3 V2 V1N1 N2 N4 N3 V4 V3 V2 V1N1 N3 N2 N4 V4 V3 V2 V1N1 N3 N4 N2 V4 V3 V2 V1N1 N4 N3 N2 V4 V3 V2 V1N1 N4 N2 N3 V4 V3 V2 V1 . . .(24 in all)

Only some of these can be generatedwith correct structural descriptionswith Tree-local MC-TAG

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Scrambling- Example 4 For k=4Some possible sequences:

N1 N2 N3 N4 V4 V3 V2 V1N4 N3 N2 N1 V4 V3 V2 V1 . . .N1 N4 N3 N2 V4 V3 V2 V1 . . .

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Scrambling- Example 4 For k=4An impossible sequence: . . .

N4 N1 N3 N2 V4 V3 V2 V1 . . .

(The status of remaining 20 sequences has not been worked out yet.)

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Scrambling – Example 4

For all k, at least the following two permutationscan always be realized by Tree-local MC-TAG

N1 N2 … Nk-1 Nk Vk Vk-1 …V1

Nk Nk-1 … N2 N1 Vk Vk-1 … V1

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Landscape analogy (not completely worked out)

All sequences for k=1,2, and 3, and for k= 4.5… the purelynested the purely crossed sequences, and possibly someothers are on the flat floor of a valley with steeply rising mountains on either side. All other sequences for k= 4,5,…are on the these steeply rising surfaces of the mountains.

(Analogy: Energy landscapes for biological sequences)

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A claim about recursion in language• All recursive constructions in language are non-uniform (NU), i.e., -- a recursive construction when viewed across all its variants is non-uniform• That is, a recursive construction, although unbounded in one or more of its variants, it is bounded when viewed across all its variants• In this sense, recursion is bounded• Note that we have not put any explicit bound in the grammar itself• The results follow from the notions of locality and flexible composition implicit in Tree-local MC-LTAG

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Psycholinguistic Relevance

• Non-uniformity of recursion indirectly bounding recursion is a competence property and not a performance property• We have not put an arbitrary external bound on recursion -- The indirect bound is a property of the grammar -- This is quite different from putting an arbitrary bound on recursion in a CFG to bound center embedding of relative clauses, for example• We are not arguing against processing constraints. Clearly, for the variants with unbounded recursion, processing constraints need to be invoked. However, the non-uniformity of recursion provides a structural bound. Thus, the non- uniformity of recursion may be indirectly bounding all recursion!

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Summary• A recursive construction is uniform if all variants of the construction generate correct semantics, otherwise, it is non-uniform• For Tree-local MC-LTAG, recursion is uniform for up to two levels of embedding, i.e., three clauses in all, beyond that it is non-uniform• A claim: All recursion in language is non-uniform, thus indirectly bounding recursion -- This bound is a formal (competence) property -- Not due to an arbitrary external bound on the grammar• A possible challenge to a foundational property of language??