Minimalist Machine Derivations

Minimalist Machine Derivations

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Examples:

T-to-C Movement: Causes and Consequences. Pesetsky & Torrego (2001). collapse

Example	Instruction stream (clickable)	Notes
(5a) What did Mary buy? (5b) *What Mary bought?	[what:n, q, buy, 'v*', [mary, d], 'Tpast', c_Q]	(5a) T to matrix C => do-support. (5b) Mary to edge C blocked (FI: exclamatory).
(5c) *Who did buy the book? (5d) Who bought the book?	[book, the, buy, 'v*', [who, q], 'Tpast', c_Q]	No do-support triggered. (5c) ruled out by economy.
(23) What will Mary buy?	[what:n, q, buy, 'v*', [mary, d], will, 'T', c_Q]	Auxilary will raises to edge of C.
(24) What did John say that Mary will buy?	[what:n, q, buy, 'v*', [mary, d], will, 'T', c_eQ, say, v_unerg, [john, d], 'Tpast', c_Q]	Two derivations: (24) T to C realized as that. Or that can be omitted. c_eQ hosts wh-movement only.
(28a) Who did John say will buy the book? (28b) *Who did John say that will buy the book?	[book, the, buy, 'v*', [who, q], will, 'T', c_eQ, say, v_unerg, [john, d], 'Tpast', c_Q]	That-trace effect. (28b) ruled out by economy.
(31) Mary thinks that Sue will buy the book (33) Mary thinks Sue will buy the book	[book, the, buy, 'v*', [sue, d], will, 'T', c_e, think, v_unerg, [mary, d], 'T', c]	Two derivations: (31) T to embedded C (c_e) realized as that. (33) c_e attracts subject Sue
(43a) *What a silly book did Mary buy! (43b) What a silly book Mary bought!	[book, silly, a, what:d, q, buy, 'v*', [mary, d], 'Tpast', c_Q]	(43a) T to C blocked by CI: exclamative. (43b) Mary in edge of C.
(47a) Bill asked what Mary bought (47b) Bill asked what did Mary buy (47c) Bill asked what that Mary bought	[what:n, q, buy, 'v*', [mary, d], 'Tpast', c_Qe, ask, v_unerg, [bill, d], 'Tpast', c]	Interrogative embedded C does not support T displacement. Note: same parse derived twice.
Extra test cases
Who was John meeting?	[who, q, meet, 'v*', [john, d], prog, 'v~', 'Tpast', c_Q]	Object wh-movement. Auxiliary be pied-piping.
Who was meeting John?	[john, d, meet, 'v*', [who, q], prog, 'v~', 'Tpast', c_Q]	Subject wh-movement. Auxiliary be pied-piping.
*Who do you think that saw John? Who do you think saw John?	[john, d, see, 'v*', [who, q], 'Tpast', c_eQ, think, 'v_unerg', [you, d], 'T', c_Q]	That-trace effect. Economy: no T to C.
Who do you think that John saw? Who do you think John saw?	[who, q, see, 'v*', [john, d], 'Tpast', c_eQ, think, 'v_unerg', [you, d], 'T', c_Q]	Two derivations. No that-trace effect with object.

Machine Parameters: expand

Animation:
(28a) Who did John say will buy the book?
(28b) *Who did John say that will buy the book?

Derivation:
(28a) Who did John say will buy the book?
(28b) *Who did John say that will buy the book?

Stream:	[[book!D],[the!case!N],[buy],[v*!phi],[[who!D],[q!case!N!scope]],[will],[T!phi],[c_eQ!wh!T],[say],[v_unerg],[[john!D],[d!case!N]],[Tpast!phi!v],[c_Q!wh!T]]
Stack (⥥):
SO:	[]

Step 1.

Head of stream [book!D] is the initial SO

Stream:	[[the!case!N],[buy],[v*!phi],[[who!D],[q!case!N!scope]],[will],[T!phi],[c_eQ!wh!T],[say],[v_unerg],[[john!D],[d!case!N]],[Tpast!phi!v],[c_Q!wh!T]]
Stack (⥥):
SO:	[book!D]

Step 2.

Merge [the!case!N] and [book!D]

Label from [the!case!N] (head with an unvalued uF)

Inherit interpretable feature(s) [f(phi,[3,sg,n])] from [book!D]

[the!case!N] values D on [book!D]

[book] values N on [the!case!N]

Stream:	[[buy],[v*!phi],[[who!D],[q!case!N!scope]],[will],[T!phi],[c_eQ!wh!T],[say],[v_unerg],[[john!D],[d!case!N]],[Tpast!phi!v],[c_Q!wh!T]]
Stack (⥥):
SO:	[the!case[the][book]]

Step 3.

Merge [buy] and [the!case[the][book]]

Label from [buy] (head merging with a non-head)

Theta-mark [the!case[the][book]]

Push [the!case[the][book]] (unvalued uF) onto stack

Stream:	[[v*!phi],[[who!D],[q!case!N!scope]],[will],[T!phi],[c_eQ!wh!T],[say],[v_unerg],[[john!D],[d!case!N]],[Tpast!phi!v],[c_Q!wh!T]]
Stack (⥥):	[the!case[the][book]]
SO:	[buy[buy][the!case[the][book]]]

Step 4.

Merge [v*!phi] and [buy[buy][the!case[the..][book..]]]

Label from [v*!phi] (head merging with a non-head)

[the!case[the][book]] values uPhi on [v*!phi]

[v*] values acc case on [the!case[the][book]]

Stream:	[[[who!D],[q!case!N!scope]],[will],[T!phi],[c_eQ!wh!T],[say],[v_unerg],[[john!D],[d!case!N]],[Tpast!phi!v],[c_Q!wh!T]]
Stack (⥥):	[the[the][book]]
SO:	[v[v][buy[buy][the[the][book]]]]

Step 5.

Begin substream

Stream:	[[who!D],[q!case!N!scope]]
Stack (⥥):
SO:	[]

Step 6.

Head of stream [who!D] is the initial SO

Stream:	[[q!case!N!scope]]
Stack (⥥):
SO:	[who!D]

Step 7.

Merge [q!case!N!scope] and [who!D]

Label from [q!case!N!scope] (head with an unvalued uF)

Inherit interpretable feature(s) [f(phi,[3,sg,n])] from [who!D]

[q!case!N!scope] values D on [who!D]

[who] values N on [q!case!N!scope]

Stream:	[]
Stack (⥥):
SO:	[q!case!scope[q!scope][who]]

End substream, SO [q!case!scope[q!scope][who]] re-inserted into main stream

Step 8.

Stream:	[[q!case!scope[q!scope][who]],[will],[T!phi],[c_eQ!wh!T],[say],[v_unerg],[[john!D],[d!case!N]],[Tpast!phi!v],[c_Q!wh!T]]
Stack (⥥):	[the[the][book]]
SO:	[v[v][buy[buy][the[the][book]]]]

Step 9.

Merge [v*[v*][buy[buy..][the..]]] and [q!case!scope[q!scope][who]]

Label from [v*[v*][buy[buy..][the..]]] (edge feature)

Theta-mark [q!case!scope[q!scope][who]]

Push [q!case!scope[q!scope][who]] (unvalued uF) onto stack

Stream:	[[will],[T!phi],[c_eQ!wh!T],[say],[v_unerg],[[john!D],[d!case!N]],[Tpast!phi!v],[c_Q!wh!T]]
Stack (⥥):	[q!case!scope[q!scope][who]] [the[the][book]]
SO:	[v[q!case!scope[q!scope][who]][v[v*][buy[buy][the[the][book]]]]]

Step 10.

Merge [will] and [v*[q!case!scope[q..][who..]][v*[v*..][buy..]]]

Label from [will] (head merging with a non-head)

Stream:	[[T!phi],[c_eQ!wh!T],[say],[v_unerg],[[john!D],[d!case!N]],[Tpast!phi!v],[c_Q!wh!T]]
Stack (⥥):	[q!case!scope[q!scope][who]] [the[the][book]]
SO:	[will[will][v[q!case!scope[q!scope][who]][v[v*][buy[buy][the[the][book]]]]]]

Step 11.

Merge [T!phi] and [will[will][v*[q..][v*..]]]

Label from [T!phi] (head merging with a non-head)

[q!case!scope[q!scope][who]] values uPhi on [T!phi]

[T] values nom case on [q!case!scope[q!scope][who]]

Stream:	[[c_eQ!wh!T],[say],[v_unerg],[[john!D],[d!case!N]],[Tpast!phi!v],[c_Q!wh!T]]
Stack (⥥):	[q!scope[q!scope][who]] [the[the][book]]
SO:	[T[T][will[will][v[q!scope[q!scope][who]][v[v*][buy[buy][the[the][book]]]]]]]

Step 12.

Internal merge selected

Merge [T[T][will[will..][v*..]]] and [q!scope[q!scope][who]]

Label from [T[T][will[will..][v*..]]] (edge feature)

Stream:	[[c_eQ!wh!T],[say],[v_unerg],[[john!D],[d!case!N]],[Tpast!phi!v],[c_Q!wh!T]]
Stack (⥥):	[q!scope[q!scope][who]] [the[the][book]]
SO:	[T[q!scope[q!scope][who]][T[T][will[will][v[q!scope[q!scope][who]][v[v*][buy[buy][the[the][book]]]]]]]]

Step 13.

Merge [c_eQ!wh!T] and [T[q!scope[q..][who..]][T[T..][will..]]]

Label from [c_eQ!wh!T] (head merging with a non-head)

[q!scope[q!scope][who]] values wh on [c_eQ!wh!T]

[q!scope[q!scope][who]] values T on [c_eQ!T] (economy)

Internal merge selected

Merge [c_eQ[c_eQ][T[q..][T..]]] and [q!scope[q!scope][who]]

Label from [c_eQ[c_eQ][T[q..][T..]]] (edge feature)

Stream:	[[say],[v_unerg],[[john!D],[d!case!N]],[Tpast!phi!v],[c_Q!wh!T]]
Stack (⥥):	[q!scope[q!scope][who]] [the[the][book]]
SO:	[c_eQ[q!scope[q!scope][who]][c_eQ[c_eQ][T[q!scope[q!scope][who]][T[T][will[will][v[q!scope[q!scope][who]][v[v*][buy[buy][the[the][book]]]]]]]]]]

Step 14.

Local Extent boundary at [c_eQ[q!scope[q..][who..]][c_eQ[c_eQ..][T..]]]

Stack element [q!scope[q!scope][who]] with unvalued uF found

New boundary (b) marker stacked

Restack [q!scope[q!scope][who]] onto stack

Stream:	[[say],[v_unerg],[[john!D],[d!case!N]],[Tpast!phi!v],[c_Q!wh!T]]
Stack (⥥):	[q!scope[q!scope][who]] b [the[the][book]]
SO:	[c_eQ[q!scope[q!scope][who]][c_eQ[c_eQ][T[q!scope[q!scope][who]][T[T][will[will][v[q!scope[q!scope][who]][v[v*][buy[buy][the[the][book]]]]]]]]]]

Step 15.

Merge [say] and [c_eQ[q!scope[q..][who..]][c_eQ[c_eQ..][T..]]]

Label from [say] (head merging with a non-head)

Theta-mark [c_eQ[q!scope[q..][who..]][c_eQ[c_eQ..][T..]]]

Stream:	[[v_unerg],[[john!D],[d!case!N]],[Tpast!phi!v],[c_Q!wh!T]]
Stack (⥥):	[q!scope[q!scope][who]] b [the[the][book]]
SO:	[say[say][c_eQ[q!scope[q!scope][who]][c_eQ[c_eQ][T[q!scope[q!scope][who]][T[T][will[will][v[q!scope[q!scope][who]][v[v*][buy[buy][the[the][book]]]]]]]]]]]

Step 16.

Merge [v_unerg] and [say[say][c_eQ[q..][c_eQ..]]]

Label from [v_unerg] (head merging with a non-head)

Stream:	[[[john!D],[d!case!N]],[Tpast!phi!v],[c_Q!wh!T]]
Stack (⥥):	[q!scope[q!scope][who]] b [the[the][book]]
SO:	[v_unerg[v_unerg][say[say][c_eQ[q!scope[q!scope][who]][c_eQ[c_eQ][T[q!scope[q!scope][who]][T[T][will[will][v[q!scope[q!scope][who]][v[v*][buy[buy][the[the][book]]]]]]]]]]]]

Step 17.

Begin substream

Stream:	[[john!D],[d!case!N]]
Stack (⥥):
SO:	[]

Step 18.

Head of stream [john!D] is the initial SO

Stream:	[[d!case!N]]
Stack (⥥):
SO:	[john!D]

Step 19.

Merge [d!case!N] and [john!D]

Label from [d!case!N] (head with an unvalued uF)

Inherit interpretable feature(s) [f(phi,[3,sg,n])] from [john!D]

[d!case!N] values D on [john!D]

[john] values N on [d!case!N]

Stream:	[]
Stack (⥥):
SO:	[d!case[d][john]]

End substream, SO [d!case[d][john]] re-inserted into main stream

Step 20.

Stream:	[[d!case[d][john]],[Tpast!phi!v],[c_Q!wh!T]]
Stack (⥥):	[q!scope[q!scope][who]] b [the[the][book]]
SO:	[v_unerg[v_unerg][say[say][c_eQ[q!scope[q!scope][who]][c_eQ[c_eQ][T[q!scope[q!scope][who]][T[T][will[will][v[q!scope[q!scope][who]][v[v*][buy[buy][the[the][book]]]]]]]]]]]]

Step 21.

Merge [v_unerg[v_unerg][say[say..][c_eQ..]]] and [d!case[d][john]]

Label from [v_unerg[v_unerg][say[say..][c_eQ..]]] (edge feature)

Theta-mark [d!case[d][john]]

Push [d!case[d][john]] (unvalued uF) onto stack

Stream:	[[Tpast!phi!v],[c_Q!wh!T]]
Stack (⥥):	[d!case[d][john]] [q!scope[q!scope][who]] b [the[the][book]]
SO:	[v_unerg[d!case[d][john]][v_unerg[v_unerg][say[say][c_eQ[q!scope[q!scope][who]][c_eQ[c_eQ][T[q!scope[q!scope][who]][T[T][will[will][v[q!scope[q!scope][who]][v[v*][buy[buy][the[the][book]]]]]]]]]]]]]

Step 22.

Merge [Tpast!phi!v] and [v_unerg[d!case[d..][john..]][v_unerg[v_unerg..][say..]]]

Label from [Tpast!phi!v] (head merging with a non-head)

[d!case[d][john]] values uPhi on [Tpast!phi!v]

[Tpast!v] values nom case on [d!case[d][john]]

Relativized TOS search for iF(v) skipping [d[d][john]]

Relativized TOS search for iF(v) skipping [q!scope[q!scope][who]]

[Tpast!v] attracts [v_unerg[d[d..][john..]][v_unerg[v_unerg..][say..]]]

Merge [Tpast[Tpast][v_unerg[d..][v_unerg..]]] and [v_unerg]

Label from [Tpast[Tpast][v_unerg[d..][v_unerg..]]] (edge feature)

Stream:	[[c_Q!wh!T]]
Stack (⥥):	[d[d][john]] [q!scope[q!scope][who]] b [the[the][book]]
SO:	[Tpast[v_unerg][Tpast[Tpast][v_unerg[d[d][john]][v_unerg[v_unerg][say[say][c_eQ[q!scope[q!scope][who]][c_eQ[c_eQ][T[q!scope[q!scope][who]][T[T][will[will][v[q!scope[q!scope][who]][v[v*][buy[buy][the[the][book]]]]]]]]]]]]]]]

Step 23.

Internal merge selected

Merge [Tpast[v_unerg][Tpast[Tpast..][v_unerg..]]] and [d[d][john]]

Label from [Tpast[v_unerg][Tpast[Tpast..][v_unerg..]]] (edge feature)

Stream:	[[c_Q!wh!T]]
Stack (⥥):	[d[d][john]] [q!scope[q!scope][who]] b [the[the][book]]
SO:	[Tpast[d[d][john]][Tpast[v_unerg][Tpast[Tpast][v_unerg[d[d][john]][v_unerg[v_unerg][say[say][c_eQ[q!scope[q!scope][who]][c_eQ[c_eQ][T[q!scope[q!scope][who]][T[T][will[will][v[q!scope[q!scope][who]][v[v*][buy[buy][the[the][book]]]]]]]]]]]]]]]]

Step 24.

Merge [c_Q!wh!T] and [Tpast[d[d..][john..]][Tpast[v_unerg..][Tpast..]]]

Label from [c_Q!wh!T] (head merging with a non-head)

Relativized TOS search for iF(wh) skipping [d[d][john]]

[q!scope[q!scope][who]] values wh on [c_Q!wh!T]

[d[d][john]] values T on [c_Q!T]

Internal merge selected

Merge [c_Q[c_Q][Tpast[d..][Tpast..]]] and [d[d][john]]

Label from [c_Q[c_Q][Tpast[d..][Tpast..]]] (edge feature)

[c_Q] values uscope on [q!scope[q!scope][who]]

Merge [c_Q[d[d..][john..]][c_Q[c_Q..][Tpast..]]] and [q[q][who]]

Label from [c_Q[d[d..][john..]][c_Q[c_Q..][Tpast..]]] (edge feature)

Stream:	[]
Stack (⥥):	[d[d][john]] [q[q][who]] b [the[the][book]]
SO:	[c_Q[q[q][who]][c_Q[d[d][john]][c_Q[c_Q][Tpast[d[d][john]][Tpast[v_unerg][Tpast[Tpast][v_unerg[d[d][john]][v_unerg[v_unerg][say[say][c_eQ[q[q][who]][c_eQ[c_eQ][T[q[q][who]][T[T][will[will][v[q[q][who]][v[v*][buy[buy][the[the][book]]]]]]]]]]]]]]]]]]]

Step 25.

Local Extent boundary at [c_Q[q[q..][who..]][c_Q[d..][c_Q..]]]

New boundary (b) marker stacked

Stream:	[]
Stack (⥥):	b [d[d][john]] [q[q][who]] b [the[the][book]]
SO:	[c_Q[q[q][who]][c_Q[d[d][john]][c_Q[c_Q][Tpast[d[d][john]][Tpast[v_unerg][Tpast[Tpast][v_unerg[d[d][john]][v_unerg[v_unerg][say[say][c_eQ[q[q][who]][c_eQ[c_eQ][T[q[q][who]][T[T][will[will][v[q[q][who]][v[v*][buy[buy][the[the][book]]]]]]]]]]]]]]]]]]]

Conceptual-Intensional (CI) Interface: [c_Q] + edge [[q[q][who]],[d[d][john]]] constitutes an ill-formed interrogative!

Backtrack

Stream:	[[c_Q!wh!T]]
Stack (⥥):	[d[d][john]] [q!scope[q!scope][who]] b [the[the][book]]
SO:	[Tpast[d[d][john]][Tpast[v_unerg][Tpast[Tpast][v_unerg[d[d][john]][v_unerg[v_unerg][say[say][c_eQ[q!scope[q!scope][who]][c_eQ[c_eQ][T[q!scope[q!scope][who]][T[T][will[will][v[q!scope[q!scope][who]][v[v*][buy[buy][the[the][book]]]]]]]]]]]]]]]]

re-doing step 24

Step 26.

[c_Q!T] attracts [Tpast[d[d..][john..]][Tpast[v_unerg..][Tpast..]]]

Internal merge selected

Merge [c_Q[c_Q][Tpast[d..][Tpast..]]] and [v_unerg]

Label from [c_Q[c_Q][Tpast[d..][Tpast..]]] (edge feature)

Merge [c_Q[v_unerg][c_Q[c_Q..][Tpast..]]] and [Tpast]

Label from [c_Q[v_unerg][c_Q[c_Q..][Tpast..]]] (edge feature)

[c_Q] values uscope on [q!scope[q!scope][who]]

Merge [c_Q[Tpast][c_Q[v_unerg..][c_Q..]]] and [q[q][who]]

Label from [c_Q[Tpast][c_Q[v_unerg..][c_Q..]]] (edge feature)

Stream:	[]
Stack (⥥):	[d[d][john]] [q[q][who]] b [the[the][book]]
SO:	[c_Q[q[q][who]][c_Q[Tpast][c_Q[v_unerg][c_Q[c_Q][Tpast[d[d][john]][Tpast[v_unerg][Tpast[Tpast][v_unerg[d[d][john]][v_unerg[v_unerg][say[say][c_eQ[q[q][who]][c_eQ[c_eQ][T[q[q][who]][T[T][will[will][v[q[q][who]][v[v*][buy[buy][the[the][book]]]]]]]]]]]]]]]]]]]]

Step 27.

Local Extent boundary at [c_Q[q[q..][who..]][c_Q[Tpast..][c_Q..]]]

New boundary (b) marker stacked

Stream:	[]
Stack (⥥):	b [d[d][john]] [q[q][who]] b [the[the][book]]
SO:	[c_Q[q[q][who]][c_Q[Tpast][c_Q[v_unerg][c_Q[c_Q][Tpast[d[d][john]][Tpast[v_unerg][Tpast[Tpast][v_unerg[d[d][john]][v_unerg[v_unerg][say[say][c_eQ[q[q][who]][c_eQ[c_eQ][T[q[q][who]][T[T][will[will][v[q[q][who]][v[v*][buy[buy][the[the][book]]]]]]]]]]]]]]]]]]]]

CI: wh-question

Parse:

Spell-out:

who -ed(sg) do john say -s will buy the book (after morpheme realization)

who do -ed(sg) john say will -s buy the book (after affix-hop)

who do -ed(sg) john say will -s buy the book (after morpheme realization, stage 2)

who did john say will buy the book

One derivation found.

Computational Cost:

Merge: 23, Agree: 18, Unify: 0, Push: 3, Boundaries: 3, Inject: 1

Non-TOS access: 3, Pop: 0, Depth cost: 36

Step:	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24	25	26	27
Stack depth:	0	0	0	1	1	0	0	0	1	2	2	2	2	2	3	3	3	0	0	0	3	4	4	4	4	5	4	5