Computational perspectives on phonological constituency and recursion

Talk at RecPhon 2019: Recursivity in Phonology below and above the word.
21-22 November 2019, Universitat Autònoma de Barcelona, Bellaterra.
Website: http://filcat.uab.cat/pagines_clt/recphon2019/

Factoring prosodic recursion Computing with trees A common idea A reason not to admit prosodic recursion: Adding prosodic recursion into phonological descriptions and computations blows up the complexity of description/computation. Why should we do this if recursion is shallow, e.g., 1 or two layers? No complexity blowup, and gains in capturing gener- alizations. K.M. Yu [email protected] Phonological constituency and recursion 2/ 41

Factoring prosodic recursion Computing with trees 1 Factoring prosodic recursion Recursion in phonology Prosodic constituents in phonology 2 Computing with trees K.M. Yu [email protected] Phonological constituency and recursion 3/ 41

Factoring prosodic recursion Computing with trees Recursion in phonology Prosodic constituents in phonology Table of Contents 1 Factoring prosodic recursion Recursion in phonology Prosodic constituents in phonology 2 Computing with trees K.M. Yu [email protected] Phonological constituency and recursion 4/ 41

Factoring prosodic recursion Computing with trees Recursion in phonology Prosodic constituents in phonology Factoring prosodic recursion 1 Uncontroversial: Recursion is in phonology K.M. Yu [email protected] Phonological constituency and recursion 5/ 41

Factoring prosodic recursion Computing with trees Recursion in phonology Prosodic constituents in phonology Factoring prosodic recursion 1 Uncontroversial: Recursion is in phonology Without recursive operations, phonological knowledge cannot be generalized to strings of arbitrary (ﬁnite) length K.M. Yu [email protected] Phonological constituency and recursion 5/ 41

Factoring prosodic recursion Computing with trees Recursion in phonology Prosodic constituents in phonology Factoring prosodic recursion 1 Uncontroversial: Recursion is in phonology Without recursive operations, phonological knowledge cannot be generalized to strings of arbitrary (ﬁnite) length With recursion, we can write grammars that recognize that a constituent shares properties with one of its parts K.M. Yu [email protected] Phonological constituency and recursion 5/ 41

Factoring prosodic recursion Computing with trees Recursion in phonology Prosodic constituents in phonology Factoring prosodic recursion 1 Uncontroversial: Recursion is in phonology Without recursive operations, phonological knowledge cannot be generalized to strings of arbitrary (ﬁnite) length With recursion, we can write grammars that recognize that a constituent shares properties with one of its parts 2 Controversial but widely assumed: Phonological grammars refer to constituents K.M. Yu [email protected] Phonological constituency and recursion 5/ 41

Factoring prosodic recursion Computing with trees Recursion in phonology Prosodic constituents in phonology Factoring prosodic recursion 1 Uncontroversial: Recursion is in phonology Without recursive operations, phonological knowledge cannot be generalized to strings of arbitrary (ﬁnite) length With recursion, we can write grammars that recognize that a constituent shares properties with one of its parts 2 Controversial but widely assumed: Phonological grammars refer to constituents Phonological patterns distinguish right-branching from left-branching K.M. Yu [email protected] Phonological constituency and recursion 5/ 41

Factoring prosodic recursion Computing with trees Recursion in phonology Prosodic constituents in phonology Factoring prosodic recursion 1 Uncontroversial: Recursion is in phonology Without recursive operations, phonological knowledge cannot be generalized to strings of arbitrary (ﬁnite) length With recursion, we can write grammars that recognize that a constituent shares properties with one of its parts 2 Controversial but widely assumed: Phonological grammars refer to constituents Phonological patterns distinguish right-branching from left-branching There are phonological patterns deﬁned over trees K.M. Yu [email protected] Phonological constituency and recursion 5/ 41

Factoring prosodic recursion Computing with trees Recursion in phonology Prosodic constituents in phonology Table of Contents 1 Factoring prosodic recursion Recursion in phonology Prosodic constituents in phonology 2 Computing with trees K.M. Yu [email protected] Phonological constituency and recursion 6/ 41

Factoring prosodic recursion Computing with trees Recursion in phonology Prosodic constituents in phonology What is recursion (informal)? Recursion: structure/operation being deﬁned used in its own deﬁnition Recursive structure: string deﬁned as an extension of another string Recursive operation: ω → σ ω K.M. Yu [email protected] Phonological constituency and recursion 7/ 41

Factoring prosodic recursion Computing with trees Recursion in phonology Prosodic constituents in phonology Simplest deﬁnition of strings is recursive Given an alphabet of symbols, Σ, deﬁne a string over Σ as follows: 1 Base case: The empty symbol λ is a string. 2 Recursive case: If w is a string and s is a symbol (s ∈ Σ), then ws is a string. Note that this deﬁnes unbounded recursion. K.M. Yu [email protected] Phonological constituency and recursion 8/ 41

Factoring prosodic recursion Computing with trees Recursion in phonology Prosodic constituents in phonology Finite physical realization of unbounded recursion Maximum length of a string in Python on a 64-bit system: 9223372036854775807 1 import sys 2 print(sys.maxsize) 3 9223372036854775807 K.M. Yu [email protected] Phonological constituency and recursion 9/ 41

Factoring prosodic recursion Computing with trees Recursion in phonology Prosodic constituents in phonology Finite physical realization of unbounded recursion Maximum length of a string in Python on a 64-bit system: 9223372036854775807 1 import sys 2 print(sys.maxsize) 3 9223372036854775807 Recursion unbounded in deﬁnition of data structure, but ﬁnite realization of structure in physical systems. K.M. Yu [email protected] Phonological constituency and recursion 9/ 41

Factoring prosodic recursion Computing with trees Recursion in phonology Prosodic constituents in phonology Non-recursive grammars generate ﬁnite sets (a) Non-recursive grammar (b) (Non-recursive) list grammar α → λ α → λ α → V γ α → V α → C β α → CV β → V γ γ → λ Generates {λ, V , CV } Generates {λ, V , CV } Without recursion, we can only write grammars that can be modeled as ﬁnite lists of words up to some upper bound in length. K.M. Yu [email protected] Phonological constituency and recursion 11/ 41

Factoring prosodic recursion Computing with trees Recursion in phonology Prosodic constituents in phonology Strings of arbitrary (ﬁnite) length Words and sentences can be arbitrarily long, (though ﬁnite) K.M. Yu [email protected] Phonological constituency and recursion 12/ 41

Factoring prosodic recursion Computing with trees Recursion in phonology Prosodic constituents in phonology Strings of arbitrary (ﬁnite) length Words and sentences can be arbitrarily long, (though ﬁnite) Winnepesaukee, Halicarnassus (Dabouis et al., this conference) K.M. Yu [email protected] Phonological constituency and recursion 12/ 41

Factoring prosodic recursion Computing with trees Recursion in phonology Prosodic constituents in phonology Strings of arbitrary (ﬁnite) length Words and sentences can be arbitrarily long, (though ﬁnite) Winnepesaukee, Halicarnassus (Dabouis et al., this conference) Winnehalipecarnasaukeessus K.M. Yu [email protected] Phonological constituency and recursion 12/ 41

Factoring prosodic recursion Computing with trees Recursion in phonology Prosodic constituents in phonology Strings of arbitrary (ﬁnite) length Words and sentences can be arbitrarily long, (though ﬁnite) Winnepesaukee, Halicarnassus (Dabouis et al., this conference) Winnehalipecarnasaukeessus There are inﬁnitely many possible words/sentences. . . K.M. Yu [email protected] Phonological constituency and recursion 12/ 41

Factoring prosodic recursion Computing with trees Recursion in phonology Prosodic constituents in phonology Strings of arbitrary (ﬁnite) length Words and sentences can be arbitrarily long, (though ﬁnite) Winnepesaukee, Halicarnassus (Dabouis et al., this conference) Winnehalipecarnasaukeessus There are inﬁnitely many possible words/sentences. . . . . . so we need grammars that can generate inﬁnite set of arbitrarily long words, i.e., grammars with recursive operations K.M. Yu [email protected] Phonological constituency and recursion 12/ 41

Factoring prosodic recursion Computing with trees Recursion in phonology Prosodic constituents in phonology Strings of arbitrary (ﬁnite) length Words and sentences can be arbitrarily long, (though ﬁnite) Winnepesaukee, Halicarnassus (Dabouis et al., this conference) Winnehalipecarnasaukeessus There are inﬁnitely many possible words/sentences. . . . . . so we need grammars that can generate inﬁnite set of arbitrarily long words, i.e., grammars with recursive operations Bounds on recursion could come from factors outside phonological grammar, e.g., processing, memory, lexi- con, or elsewhere in phonological grammar, e.g., con- straint interactions K.M. Yu [email protected] Phonological constituency and recursion 12/ 41

Factoring prosodic recursion Computing with trees Recursion in phonology Prosodic constituents in phonology Two derivations of CV With non-recursive grammar With recursive grammar α C β V γ λ α C β V α λ α γ V β C V α V β C V K.M. Yu [email protected] Phonological constituency and recursion 14/ 41

Factoring prosodic recursion Computing with trees Recursion in phonology Prosodic constituents in phonology Recursive operations in phonological grammars II (a) Non-recursive grammar α → λ α → λ, α → V γ, α → C β, β → V γ γ → λ, γ → V , γ → C δ, δ → V Generates {λ, α γ V β C ε V δ C V V K.M. Yu [email protected] Phonological constituency and recursion 15/ 41

Factoring prosodic recursion Computing with trees Recursion in phonology Prosodic constituents in phonology Recursive operations in phonological grammars II (a) Non-recursive grammar α → λ α → λ, α → V γ, α → C β, β → V γ γ → λ, γ → V , γ → C δ, δ → V Generates {λ, (C)V , α γ V β C ε V δ C V V K.M. Yu [email protected] Phonological constituency and recursion 15/ 41

Factoring prosodic recursion Computing with trees Recursion in phonology Prosodic constituents in phonology Recursive operations in phonological grammars II (a) Non-recursive grammar α → λ α → λ, α → V γ, α → C β, β → V γ γ → λ, γ → V , γ → C δ, δ → V Generates {λ, (C)V , (C)V (C)V , α γ V β C ε V δ C V V K.M. Yu [email protected] Phonological constituency and recursion 15/ 41

Factoring prosodic recursion Computing with trees Recursion in phonology Prosodic constituents in phonology Recursive operations in phonological grammars II (a) Non-recursive grammar (b) Recursive grammar α → λ α → λ α → λ, α → V γ, α → C β, β → V γ α → V α γ → λ, γ → V , γ → C δ, δ → V α → C β β → V α Generates {λ, (C)V , Generates {(C)V }∗ (C)V (C)V , (C)V (C)V (C)V } α γ V β C ε V δ C V V α V β C V K.M. Yu [email protected] Phonological constituency and recursion 15/ 41

Factoring prosodic recursion Computing with trees Recursion in phonology Prosodic constituents in phonology Two derivations of VCV With non-recursive grammar With recursive grammar α V γ C δ V λ α V β C α V α λ K.M. Yu [email protected] Phonological constituency and recursion 16/ 41

Factoring prosodic recursion Computing with trees Recursion in phonology Prosodic constituents in phonology Two derivations of VCV With non-recursive grammar With recursive grammar α V γ C δ V λ α V β C α V α λ Non-recursive derivation can’t assign same category to diﬀerent (C)V chunks in string. The fact that (C)V can be repeated appears accidental. K.M. Yu [email protected] Phonological constituency and recursion 16/ 41

Factoring prosodic recursion Computing with trees Recursion in phonology Prosodic constituents in phonology Recursive operations in phonological grammars III (a) Non-recursive grammar (b) Recursive grammar α → λ α → λ α → λ, α → V γ, α → C β, β → V γ α → V α γ → λ, γ → V , γ → C δ, δ → V α → C β → λ, → V η, → C ζ, η → V λ β → V α Generates {λ, Generates {(C)V }∗ α γ V β C ε V δ C η V ζ C V V V α V β C V K.M. Yu [email protected] Phonological constituency and recursion 17/ 41

Factoring prosodic recursion Computing with trees Recursion in phonology Prosodic constituents in phonology Recursive operations in phonological grammars III (a) Non-recursive grammar (b) Recursive grammar α → λ α → λ α → λ, α → V γ, α → C β, β → V γ α → V α γ → λ, γ → V , γ → C δ, δ → V α → C β → λ, → V η, → C ζ, η → V λ β → V α Generates {λ, (C)V , Generates {(C)V }∗ α γ V β C ε V δ C η V ζ C V V V α V β C V K.M. Yu [email protected] Phonological constituency and recursion 17/ 41

Factoring prosodic recursion Computing with trees Recursion in phonology Prosodic constituents in phonology Recursive operations in phonological grammars III (a) Non-recursive grammar (b) Recursive grammar α → λ α → λ α → λ, α → V γ, α → C β, β → V γ α → V α γ → λ, γ → V , γ → C δ, δ → V α → C β → λ, → V η, → C ζ, η → V λ β → V α Generates {λ, (C)V , Generates {(C)V }∗ (C)V (C)V , α γ V β C ε V δ C η V ζ C V V V α V β C V K.M. Yu [email protected] Phonological constituency and recursion 17/ 41

Factoring prosodic recursion Computing with trees Recursion in phonology Prosodic constituents in phonology Recursive operations in phonological grammars III (a) Non-recursive grammar (b) Recursive grammar α → λ α → λ α → λ, α → V γ, α → C β, β → V γ α → V α γ → λ, γ → V , γ → C δ, δ → V α → C β → λ, → V η, → C ζ, η → V λ β → V α Generates {λ, (C)V , Generates {(C)V }∗ (C)V (C)V , (C)V (C)V (C)V } α γ V β C ε V δ C η V ζ C V V V α V β C V K.M. Yu [email protected] Phonological constituency and recursion 17/ 41

Factoring prosodic recursion Computing with trees Recursion in phonology Prosodic constituents in phonology Two derivations of VCVCV With non-recursive grammar With recursive grammar α V γ C δ V C ζ V η λ α V β C α V β C α V α λ K.M. Yu [email protected] Phonological constituency and recursion 18/ 41

Factoring prosodic recursion Computing with trees Recursion in phonology Prosodic constituents in phonology Two derivations of VCVCV With non-recursive grammar With recursive grammar α V γ C δ V C ζ V η λ α V β C α V β C α V α λ Recursive grammar: restriction to (C)V chunks not an accident. K.M. Yu [email protected] Phonological constituency and recursion 18/ 41

Factoring prosodic recursion Computing with trees Recursion in phonology Prosodic constituents in phonology Strategic labelling doesn’t capture generalization With non-recursive grammar With recursive grammar α1 V α2 C β2 V α3 C β3 V α4 λ α V β C α V β C α V α λ α1 α2 V β1 C α3 V β2 C α4 V β3 C V V V α V β C V K.M. Yu [email protected] Phonological constituency and recursion 19/ 41

Factoring prosodic recursion Computing with trees Recursion in phonology Prosodic constituents in phonology Recursive operations in grammar is always an analytic choice α1 α2 V β1 C α3 V β2 C α4 V β3 C V V V α V β C V Humans are ﬁnite machines so recursion in human language is always bounded (in phonology and morphosyntax) We can always model bounded recursion without recursive operations K.M. Yu [email protected] Phonological constituency and recursion 20/ 41

Factoring prosodic recursion Computing with trees Recursion in phonology Prosodic constituents in phonology Recursive operations in grammar is always an analytic choice α1 α2 V β1 C α3 V β2 C α4 V β3 C V V V α V β C V Humans are ﬁnite machines so recursion in human language is always bounded (in phonology and morphosyntax) We can always model bounded recursion without recursive operations Recursion is the analytic choice to make if we want to explain why repeatedly observed patterns are not accidental K.M. Yu [email protected] Phonological constituency and recursion 20/ 41

Factoring prosodic recursion Computing with trees Recursion in phonology Prosodic constituents in phonology Interim summary: factoring prosodic recursion 1 Uncontroversial: Recursion is in phonology. Without recursive operations, phonological knowledge cannot be generalized to strings of arbitrary (ﬁnite) length. . . . . . regardless of what lexical elements and categories we deﬁne phonological grammars over K.M. Yu [email protected] Phonological constituency and recursion 21/ 41

Factoring prosodic recursion Computing with trees Recursion in phonology Prosodic constituents in phonology Interim summary: factoring prosodic recursion 1 Uncontroversial: Recursion is in phonology. Without recursive operations, phonological knowledge cannot be generalized to strings of arbitrary (ﬁnite) length. . . . . . regardless of what lexical elements and categories we deﬁne phonological grammars over With recursion, we can write grammars that recognize that that a constituent shares properties with one of its parts K.M. Yu [email protected] Phonological constituency and recursion 21/ 41

Factoring prosodic recursion Computing with trees Recursion in phonology Prosodic constituents in phonology Interim summary: factoring prosodic recursion 1 Uncontroversial: Recursion is in phonology. Without recursive operations, phonological knowledge cannot be generalized to strings of arbitrary (ﬁnite) length. . . . . . regardless of what lexical elements and categories we deﬁne phonological grammars over With recursion, we can write grammars that recognize that that a constituent shares properties with one of its parts Whether or not we have identiﬁed the right constituents is an independent, empirical issue K.M. Yu [email protected] Phonological constituency and recursion 21/ 41

Factoring prosodic recursion Computing with trees Recursion in phonology Prosodic constituents in phonology Table of Contents 1 Factoring prosodic recursion Recursion in phonology Prosodic constituents in phonology 2 Computing with trees K.M. Yu [email protected] Phonological constituency and recursion 22/ 41

Factoring prosodic recursion Computing with trees Recursion in phonology Prosodic constituents in phonology Recursion over the “wrong” constituents With recursion, we can write grammars that recognize that the properties of a constituent is similar to one of its parts. . . α V β C α V β C α V α λ α category: {[VCVCV], VC[VCV], VCVC[V] } are V-initial K.M. Yu [email protected] Phonological constituency and recursion 23/ 41

Factoring prosodic recursion Computing with trees Recursion in phonology Prosodic constituents in phonology Recursion over the “wrong” constituents With recursion, we can write grammars that recognize that the properties of a constituent is similar to one of its parts. . . α V β C α V β C α V α λ α category: {[VCVCV], VC[VCV], VCVC[V] } are V-initial β category: { V[CVCV], VCV[CV] } are C-initial K.M. Yu [email protected] Phonological constituency and recursion 23/ 41

Factoring prosodic recursion Computing with trees Recursion in phonology Prosodic constituents in phonology Recursion over the “wrong” constituents With recursion, we can write grammars that recognize that the properties of a constituent is similar to one of its parts. . . α V β C α V β C α V α λ α category: {[VCVCV], VC[VCV], VCVC[V] } are V-initial β category: { V[CVCV], VCV[CV] } are C-initial Neither category picks out [V][CV][CV] or [VC][VC][V] K.M. Yu [email protected] Phonological constituency and recursion 23/ 41

Factoring prosodic recursion Computing with trees Recursion in phonology Prosodic constituents in phonology Recursion over the “wrong” constituents With recursion, we can write grammars that recognize that the properties of a constituent is similar to one of its parts. . . α V β C α V β C α V α λ α category: {[VCVCV], VC[VCV], VCVC[V] } are V-initial β category: { V[CVCV], VCV[CV] } are C-initial Neither category picks out [V][CV][CV] or [VC][VC][V] If we want syllables, the gram- mars we wrote won’t give us them: only suﬃxes! K.M. Yu [email protected] Phonological constituency and recursion 23/ 41

Factoring prosodic recursion Computing with trees Recursion in phonology Prosodic constituents in phonology Constituents captured by recursive grammar α V β C α V β C α V α λ VCVC[V] K.M. Yu [email protected] Phonological constituency and recursion 24/ 41

Factoring prosodic recursion Computing with trees Recursion in phonology Prosodic constituents in phonology Constituents captured by recursive grammar α V β C α V β C α V α λ VCVC[V] VCV[C[V]] K.M. Yu [email protected] Phonological constituency and recursion 24/ 41

Factoring prosodic recursion Computing with trees Recursion in phonology Prosodic constituents in phonology Constituents captured by recursive grammar α V β C α V β C α V α λ VCVC[V] VCV[C[V]] VC[V[C[V]]] K.M. Yu [email protected] Phonological constituency and recursion 24/ 41

Factoring prosodic recursion Computing with trees Recursion in phonology Prosodic constituents in phonology Constituents captured by recursive grammar α V β C α V β C α V α λ VCVC[V] VCV[C[V]] VC[V[C[V]]] V[C[V[C[V]]]] K.M. Yu [email protected] Phonological constituency and recursion 24/ 41

Factoring prosodic recursion Computing with trees Recursion in phonology Prosodic constituents in phonology Constituents captured by recursive grammar α V β C α V β C α V α λ VCVC[V] VCV[C[V]] VC[V[C[V]]] V[C[V[C[V]]]] [V[C[V[C[V]]]]] K.M. Yu [email protected] Phonological constituency and recursion 24/ 41

Factoring prosodic recursion Computing with trees Recursion in phonology Prosodic constituents in phonology Trees as additional data structures for phonology Simply put, if the representations are right, then the rules will follow. (McCarthy 1988: 84) K.M. Yu [email protected] Phonological constituency and recursion 25/ 41

Factoring prosodic recursion Computing with trees Recursion in phonology Prosodic constituents in phonology Trees as additional data structures for phonology Simply put, if the representations are right, then the rules will follow. (McCarthy 1988: 84) With trees over categories as phonological data structures (in addition to strings): Prosodic constituents follow (with deﬁnition of prosodic categories) Behavior referencing prosodic constituents (including that a constituent shares properties with one of its parts) follows Distinctions between left- and right-branching phonological structures follow Behavior referencing (non-) maximal/minimal projections in phonological trees follows K.M. Yu [email protected] Phonological constituency and recursion 25/ 41

Factoring prosodic recursion Computing with trees Recursion in phonology Prosodic constituents in phonology Trees as a data structure is always an analytic choice Modeling (recursion over) prosodic constituents using trees rather than strings is always an analytic choice. Humans are ﬁnite machines so recursion in human language is always bounded (in phonology and morphosyntax) We can always model bounded recursion over constituents without recursive operations by marking up strings with boundary symbols (and this is commonly done in natural language processing) K.M. Yu [email protected] Phonological constituency and recursion 26/ 41

Factoring prosodic recursion Computing with trees Recursion in phonology Prosodic constituents in phonology Trees as a data structure is always an analytic choice Modeling (recursion over) prosodic constituents using trees rather than strings is always an analytic choice. Humans are ﬁnite machines so recursion in human language is always bounded (in phonology and morphosyntax) We can always model bounded recursion over constituents without recursive operations by marking up strings with boundary symbols (and this is commonly done in natural language processing) Trees are the analytic choice to make if we want to explain why repeatedly observed patterns conditioned on diﬀerent natural properties of trees are not accidental K.M. Yu [email protected] Phonological constituency and recursion 26/ 41

Factoring prosodic recursion Computing with trees Recursion in phonology Prosodic constituents in phonology Prosodic constituents with string markup Yu (2019): computation of Samoan prosodic and syntax-prosody interface constraints implemented prosodic constituents with string markup K.M. Yu [email protected] Phonological constituency and recursion 27/ 41

Factoring prosodic recursion Computing with trees Recursion in phonology Prosodic constituents in phonology Prosodic constituents with string markup Yu (2019): computation of Samoan prosodic and syntax-prosody interface constraints implemented prosodic constituents with string markup K.M. Yu [email protected] Phonological constituency and recursion 27/ 41

Factoring prosodic recursion Computing with trees Recursion in phonology Prosodic constituents in phonology Prosodic tree candidates K.M. Yu [email protected] Phonological constituency and recursion 28/ 41

Factoring prosodic recursion Computing with trees Recursion in phonology Prosodic constituents in phonology Prosodic tree candidates as strings +-U[L,na]+ZYX+U[L,le]x+X+U[L,le]xy+{U[L, +-ZU[L,na]+YX+U[L,le]x+X+U[L,le]xyz+{U[L K.M. Yu [email protected] Phonological constituency and recursion 29/ 41

Factoring prosodic recursion Computing with trees Recursion in phonology Prosodic constituents in phonology Prosodic tree candidates as strings +-U[L,na]+ZYX+U[L,le]x+X+U[L,le]xy+{U[L, +-ZU[L,na]+YX+U[L,le]x+X+U[L,le]xyz+{U[L Modeling (recursion over) prosodic constituents using strings makes the constituents appear accidental. K.M. Yu [email protected]ist.umass.edu Phonological constituency and recursion 29/ 41

Factoring prosodic recursion Computing with trees Recursion in phonology Prosodic constituents in phonology Putting it together: prosodic recursion 1 Uncontroversial: Recursion is in phonology Without recursive operations, phonological knowledge cannot be generalized to strings of arbitrary (ﬁnite) length With recursion, we can write grammars that recognize that a constituent shares properties with one of its parts K.M. Yu [email protected] Phonological constituency and recursion 30/ 41

Factoring prosodic recursion Computing with trees Recursion in phonology Prosodic constituents in phonology Putting it together: prosodic recursion 1 Uncontroversial: Recursion is in phonology Without recursive operations, phonological knowledge cannot be generalized to strings of arbitrary (ﬁnite) length With recursion, we can write grammars that recognize that a constituent shares properties with one of its parts 2 Controversial but widely assumed: Phonological grammars refer to constituents There are phonological patterns deﬁned over trees K.M. Yu [email protected] Phonological constituency and recursion 30/ 41

Factoring prosodic recursion Computing with trees Recursion in phonology Prosodic constituents in phonology Putting it together: prosodic recursion 1 Uncontroversial: Recursion is in phonology Without recursive operations, phonological knowledge cannot be generalized to strings of arbitrary (ﬁnite) length With recursion, we can write grammars that recognize that a constituent shares properties with one of its parts 2 Controversial but widely assumed: Phonological grammars refer to constituents There are phonological patterns deﬁned over trees Analytic choices of recursive operations over trees as data structures make empirical generalizations non- accidental. K.M. Yu [email protected] Phonological constituency and recursion 30/ 41

Factoring prosodic recursion Computing with trees Table of Contents 1 Factoring prosodic recursion Recursion in phonology Prosodic constituents in phonology 2 Computing with trees K.M. Yu [email protected] Phonological constituency and recursion 31/ 41

Factoring prosodic recursion Computing with trees Computing with strings for ﬁnitely bounded recursion So long as there is a ﬁnite bound on recursion, we have the choice of computing on strings to approximate computing on trees K.M. Yu [email protected] Phonological constituency and recursion 32/ 41

Factoring prosodic recursion Computing with trees Computing with strings for ﬁnitely bounded recursion So long as there is a ﬁnite bound on recursion, we have the choice of computing on strings to approximate computing on trees But we have to count each additional layer and it becomes an accident if a subpart of a constituent shares properties with the constituent K.M. Yu [email protected] Phonological constituency and recursion 32/ 41

Factoring prosodic recursion Computing with trees Computing with strings for ﬁnitely bounded recursion So long as there is a ﬁnite bound on recursion, we have the choice of computing on strings to approximate computing on trees But we have to count each additional layer and it becomes an accident if a subpart of a constituent shares properties with the constituent What about a potential blowup in complexity from computing over trees? K.M. Yu [email protected] Phonological constituency and recursion 32/ 41

Factoring prosodic recursion Computing with trees Computing operations on trees Two or more, use a for. Operations on trees are computed using tree transducers that transduce input trees into output trees Many tree transducers can be computed in linear time in the size of the tree Case study: syntax-prosody mapping in Japanese nominals (Ito and Mester 2013) K.M. Yu [email protected] Phonological constituency and recursion 33/ 41

Factoring prosodic recursion Computing with trees TATA tree transducer reference K.M. Yu [email protected] Phonological constituency and recursion 34/ 41

Factoring prosodic recursion Computing with trees Syntax-prosody mapping in Japanese nominals [ [NPposs ] NP ] structures (Ito and Mester 2013) N-gen N conj ‘and Hiroshima/Okayama ﬁsh/eggs’ A = accented ω, U = unaccented ω [[U]U] [[hiroshima no ] sakana to] (ϕ U U) [[A]A] [[okayama no ] tamago to] (ϕ U A) [[U]A] [[hiroshima no ] tamago to] (ϕ (ϕ A) (ϕ A)) [[A]U] [[okayama no ] sakana to] (ϕ (ϕ A) (ϕ U)) K.M. Yu [email protected] Phonological constituency and recursion 35/ 41

Factoring prosodic recursion Computing with trees Analysis: interleaved phonological and interface constraints Task: given an input like U U, determine the prosodic structure by computing the violations incurred by the following constraints Accent-as-Head, Lapse(ϕ) prosody Minimal Binarity(ϕ) prosody Match XP to ϕ syntax-prosody interface NoRecursion prosody K.M. Yu [email protected] Phonological constituency and recursion 36/ 41

Factoring prosodic recursion Computing with trees Computation of syntax-prosody mapping over trees: conceptual DP NP NPposs Nposs okayama-no N sakana-to D K.M. Yu [email protected] Phonological constituency and recursion 37/ 41

Factoring prosodic recursion Computing with trees Computation of syntax-prosody mapping over trees: conceptual DP/NP NPposs Nposs okayama-no N sakana-to K.M. Yu [email protected] Phonological constituency and recursion 37/ 41

Factoring prosodic recursion Computing with trees Computation of syntax-prosody mapping over trees: implementation Idea: transduce from syntactic tree to candidate prosodic trees, with some transduction rules incurring violations K.M. Yu [email protected] Phonological constituency and recursion 38/ 41

Factoring prosodic recursion Computing with trees Computation of syntax-prosody mapping over trees: implementation Idea: transduce from syntactic tree to candidate prosodic trees, with some transduction rules incurring violations K.M. Yu [email protected] Phonological constituency and recursion 38/ 41

Factoring prosodic recursion Computing with trees Computation of syntax-prosody mapping over trees: implementation Idea: transduce from syntactic tree to candidate prosodic trees, with some transduction rules incurring violations K.M. Yu [email protected] Phonological constituency and recursion 38/ 41

Factoring prosodic recursion Computing with trees Computation of syntax-prosody mapping over trees: implementation Idea: transduce from syntactic tree to candidate prosodic trees, with some transduction rules incurring violations K.M. Yu [email protected] Phonological constituency and recursion 38/ 41

Factoring prosodic recursion Computing with trees Computation of syntax-prosody mapping over trees: implementation Idea: transduce from syntactic tree to candidate prosodic trees, with some transduction rules incurring violations K.M. Yu [email protected] Phonological constituency and recursion 38/ 41

Factoring prosodic recursion Computing with trees Computation of syntax-prosody mapping over trees: implementation Idea: transduce from syntactic tree to candidate prosodic trees, with some transduction rules incurring violations K.M. Yu [email protected] Phonological constituency and recursion 38/ 41

Factoring prosodic recursion Computing with trees Computation of syntax-prosody mapping over trees: implementation Idea: transduce from syntactic tree to candidate prosodic trees, with some transduction rules incurring violations K.M. Yu [email protected] Phonological constituency and recursion 38/ 41

Factoring prosodic recursion Computing with trees Computation of syntax-prosody mapping over trees: implementation Idea: transduce from syntactic tree to candidate prosodic trees, with some transduction rules incurring violations K.M. Yu [email protected] Phonological constituency and recursion 38/ 41

Factoring prosodic recursion Computing with trees Computation of syntax-prosody mapping over trees: implementation Idea: transduce from syntactic tree to candidate prosodic trees, with some transduction rules incurring violations K.M. Yu [email protected] Phonological constituency and recursion 38/ 41

Factoring prosodic recursion Computing with trees Computation of syntax-prosody mapping over trees: implementation Idea: transduce from syntactic tree to candidate prosodic trees, with some transduction rules incurring violations K.M. Yu [email protected] Phonological constituency and recursion 38/ 41

Factoring prosodic recursion Computing with trees Computation of syntax-prosody mapping over trees: implementation Idea: transduce from syntactic tree to candidate prosodic trees, with some transduction rules incurring violations K.M. Yu [email protected] Phonological constituency and recursion 38/ 41

Factoring prosodic recursion Computing with trees Computation of syntax-prosody mapping over trees: implementation Idea: transduce from syntactic tree to candidate prosodic trees, with some transduction rules incurring violations K.M. Yu [email protected]ist.umass.edu Phonological constituency and recursion 38/ 41

Factoring prosodic recursion Computing with trees Computation of syntax-prosody mapping over trees: implementation Idea: transduce from syntactic tree to candidate prosodic trees, with some transduction rules incurring violations K.M. Yu [email protected] Phonological constituency and recursion 38/ 41

Factoring prosodic recursion Computing with trees Computation of syntax-prosody mapping over trees: implementation Idea: transduce from syntactic tree to candidate prosodic trees, with some transduction rules incurring violations K.M. Yu [email protected] Phonological constituency and recursion 38/ 41

Factoring prosodic recursion Computing with trees Computation of syntax-prosody mapping over trees: implementation Idea: transduce from syntactic tree to candidate prosodic trees, with some transduction rules incurring violations K.M. Yu [email protected] Phonological constituency and recursion 38/ 41

Factoring prosodic recursion Computing with trees Computation of syntax-prosody mapping over trees: implementation Idea: transduce from syntactic tree to candidate prosodic trees, with some transduction rules incurring violations K.M. Yu [email protected] Phonological constituency and recursion 38/ 41

Factoring prosodic recursion Computing with trees Computation of syntax-prosody mapping over trees: implementation Idea: transduce from syntactic tree to candidate prosodic trees, with some transduction rules incurring violations K.M. Yu [email protected] Phonological constituency and recursion 38/ 41

Factoring prosodic recursion Computing with trees Computation of syntax-prosody mapping over trees: implementation Idea: transduce from syntactic tree to candidate prosodic trees, with some transduction rules incurring violations K.M. Yu [email protected] Phonological constituency and recursion 38/ 41

Factoring prosodic recursion Computing with trees Computation of phonological constraints over trees Idea: transduce from input candidate prosodic tree to output candidate prosodic tree (identity transduction), but with some transduction rules incurring violations K.M. Yu [email protected] Phonological constituency and recursion 39/ 41

Factoring prosodic recursion Computing with trees Computation of phonological constraints over trees Idea: transduce from input candidate prosodic tree to output candidate prosodic tree (identity transduction), but with some transduction rules incurring violations K.M. Yu [email protected] Phonological constituency and recursion 39/ 41

Factoring prosodic recursion Computing with trees Computation of phonological constraints over trees Idea: transduce from input candidate prosodic tree to output candidate prosodic tree (identity transduction), but with some transduction rules incurring violations K.M. Yu [email protected] Phonological constituency and recursion 39/ 41

Factoring prosodic recursion Computing with trees Computation of phonological constraints over trees Idea: transduce from input candidate prosodic tree to output candidate prosodic tree (identity transduction), but with some transduction rules incurring violations K.M. Yu [email protected] Phonological constituency and recursion 39/ 41

Factoring prosodic recursion Computing with trees Computation of phonological constraints over trees Idea: transduce from input candidate prosodic tree to output candidate prosodic tree (identity transduction), but with some transduction rules incurring violations K.M. Yu [email protected] Phonological constituency and recursion 39/ 41

Factoring prosodic recursion Computing with trees Computation of phonological constraints over trees Idea: transduce from input candidate prosodic tree to output candidate prosodic tree (identity transduction), but with some transduction rules incurring violations K.M. Yu [email protected] Phonological constituency and recursion 39/ 41

Factoring prosodic recursion Computing with trees Computation of phonological constraints over trees Accent-as-Head, Minimal Binarity(ϕ), NoRecursion K.M. Yu [email protected] Phonological constituency and recursion 40/ 41

Factoring prosodic recursion Computing with trees Computation of phonological constraints over trees Accent-as-Head, Minimal Binarity(ϕ), NoRecursion K.M. Yu [email protected] Phonological constituency and recursion 40/ 41

Factoring prosodic recursion Computing with trees Computation of phonological constraints over trees Accent-as-Head, Minimal Binarity(ϕ), NoRecursion K.M. Yu [email protected] Phonological constituency and recursion 40/ 41

Factoring prosodic recursion Computing with trees Computation of phonological constraints over trees Accent-as-Head, Minimal Binarity(ϕ), NoRecursion K.M. Yu [email protected] Phonological constituency and recursion 40/ 41

Factoring prosodic recursion Computing with trees Computation of phonological constraints over trees Accent-as-Head, Minimal Binarity(ϕ), NoRecursion K.M. Yu [email protected] Phonological constituency and recursion 40/ 41

Factoring prosodic recursion Computing with trees Computation of phonological constraints over trees Accent-as-Head, Minimal Binarity(ϕ), NoRecursion K.M. Yu [email protected] Phonological constituency and recursion 40/ 41

Factoring prosodic recursion Computing with trees Computation of phonological constraints over trees Accent-as-Head, Minimal Binarity(ϕ), NoRecursion K.M. Yu [email protected] Phonological constituency and recursion 40/ 41

Factoring prosodic recursion Computing with trees Conclusion Prosodic recursion in human language is always ﬁnitely bounded and can always be modeled over strings K.M. Yu [email protected] Phonological constituency and recursion 41/ 41

Factoring prosodic recursion Computing with trees Conclusion Prosodic recursion in human language is always ﬁnitely bounded and can always be modeled over strings Analytic choices of recursive operations over trees as data structures make empirical generalizations non-accidental K.M. Yu [email protected] Phonological constituency and recursion 41/ 41

Factoring prosodic recursion Computing with trees Conclusion Prosodic recursion in human language is always ﬁnitely bounded and can always be modeled over strings Analytic choices of recursive operations over trees as data structures make empirical generalizations non-accidental Computation of syntax-prosody interface and phonological constraints over trees is feasible and may lead to new insights K.M. Yu [email protected] Phonological constituency and recursion 41/ 41