A Tale of Recursion (A very preliminary version) ARAVIND K. JOSHI

1. A Tale of Recursion (A very preliminary version) ARAVIND K. JOSHI April 19 2006 (revised May 8 2006)

2. Recursion as the unique property of the faculty of language Hauser, M.D., Chomsky, N., and Fitch, W.T. 2002 The Faculty of 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

3. 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.)

4. 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 variantsWe will call this property non-uniformity of recursionThus our claim will be thatlanguage has recursion but it is non-uniform Thus recursion is indirectly bounded!

5. An alternate perspectives on LTAG: • Flexible composition

6. Flexible Composition Adjoining as Wrapping a at x Split a: X X X a1: supertree of a at X a2: subtree of a at X

7. Flexible Composition Adjoining as Wrapping X b: a: X X a1: supertree of a at X X g: b X a2: subtree of a at X a wrapped around b i.e., the two components a1 and a2 are wrapped around b

8. Flexible Composition Wrapping as substitutions and adjunctions S b: a: S S NP(wh)¯ VP NP¯ VP NP¯ V S* V NP¯ think substitution likes e - We can also view this composition as awrapped around b - Flexible composition adjoining

9. Flexible Composition Wrapping as substitutions and adjunctions a: S substitution a1: S adjoining b: S* NP(wh)¯ S a2: VP NP¯ VP NP¯ V S* V NP¯ think likes e a1 and a2 are the two components of a a1 attached (adjoined) to the root node S of b a2 attached (substituted) at the foot node S of b Leads to multi-component TAG (MC-TAG)

10. Multi-component LTAG (MC-LTAG) a: a1: b: b: a2: • The two components are used together in one composition • step. Both components attach to nodes in b, 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.

11. 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

12. Extraposition from NP: An example (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 womanwho had lost her keyskept calling all day finally came. *(2’) The gardener who the woman kept calling all day finally came who had lost her keys.

13. S NP VP The gardener finally came S S S who the woman kept calling all day NP VP The gardener finally came

14. S { b11 b12} b1: ID NP S NP VP NP* S(i) S* S(i) finally came e NP who the woman kept calling all day The gardener S S S who the woman kept calling all day NP VP The gardener finally came

15. 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 * S S (i) S who had lost her keys NP VP finally came NP S The gardener who the woman (i) kept calling all day

16. 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

17. Uniform and non-uniform recursion • The President will resign today • John thinks the President will resign today • The President, John thinks, will resign today • Mary believesJohn thinks the President will resign today • *(5) Mary believes the President, John thinks, will resign today • *(6) The President, Mary believesJohn thinks, will resign today • This non-uniformity of recursive embedding of verbs taking clausal complements can also be modeled by tree-local MC-LTAG

18. Another example – Example 3 • Who did Bill invite? • Who does John think Bill invited? • ? (3) Who did Bill, John thinks, invite? • (4) Who does Harry believeJohnthinks Bill invited? • ?? (5) Who does Harry believe Bill, John thinks, invited? • ?? (6) Who did Bill, Harry believesJohn, thinks, invite?

19. (1) Hans1 Peter2 Marie3 schwimmen3 lassen2 sah1 Scrambling (Example 4) (2)) P(N1, N2 … Nk) Vk Vk-1 … V1where P is a permutation of k nouns • 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 asvariants of (3) • We now have the interesting result …

20. 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., correctsemantics 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

21. Scrambling- Example 4 • For k=3, all permutations on N’s are possibleN1 N2 N3 V3 V2 V1 • N1 N3 N2 V3 V2 V1 • N2 N1 N3 V3 V2 V1 • N2 N3 N1 V3 V2 V1 • N3 N1 N2 V3 V2 V1 • N3 N2 N1 V3 V2 V1

22. Some elementary trees (possibly multi-component) for a verb with a scrambled argument b1: b3: b2: b31: VP VP VP Ni VP* Ni VP Ni VP VP VP b32: VP Ni VP* VP Ni VP* VP Ni VP e e e V V V

23. N1N2N3 V3 V2V1 VP VP VP N3 VP N1 VP N2 VP VP VP VP N1 VP* VP N2 VP* VP N3 VP e e e V1 V2 V3

24. N2N3N1 V3 V2V1 VP VP VP N3 VP* N1 VP* N2 VP VP VP VP N1 VP* VP N2 VP* VP N3 VP e e e V1 V2 V3 Now how does the top level subordinator compose?

25. N2N3N1 V3 V2V1 ( top level subordinator) a a1 a2 a3 VP VP VP VP N3 VP* NP VP* N2 VP XP VP* VP VP VP VP* N1 VP* VP N2 VP* VP N3 VP e e e V1 V2 V3 a3 composes with a2, a1 with a and then the result with a2

26. Scrambling- Example 4 For k=4 N1 N2 N3 N4 V4 V3 V2 V1 N1 N2 N4 N3 V4 V3 V2 V1 N1 N3 N2 N4 V4 V3 V2 V1 N1 N3 N4 N2 V4 V3 V2 V1 N1 N4 N3 N2 V4 V3 V2 V1 N1 N4 N2 N3 V4 V3 V2 V1 . . . (24 in all) Only some of these can be generatedwith correct structural descriptionswith Tree-local MC-TAG

27. Scrambling- Example 4 For k=4 Some possible sequences: N1 N2 N3 N4 V4 V3 V2 V1 N4 N3 N2 N1 V4 V3 V2 V1 . . . N1 N4 N3 N2 V4 V3 V2 V1 . . .

28. Scrambling- Example 4 For k=4 An impossible sequence: . . . N4 N1 N3 N2 V4 V3 V2 V1 . . . (The status of remaining 20 sequences has not been worked out yet.)

29. 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

30. 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)

31. 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 localityand flexible composition implicit in Tree-local MC-LTAG

32. Psycholinguistic Relevance • Non-uniformity of recursion indirectly boundingrecursion 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!

33. 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??