Minimalist Machine Derivations

Minimalist Machine Derivations

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Examples:

Modeling of Coreference Relations in Multi-Object Constructions. (Fong & Ginsburg, 2012b). collapse

Example	Instruction stream (clickable)	Notes
(2)(a) I showed John₁ himself₁ in the mirror	[john, d, he, self, 'G', [mirror, the, in], show, 'v*', [i, d], 'Tpast', c]	Determiner self heads a Local Extent (LE). Doubling constituent (DC) self-he-John triggers stacking of John. TOS John is merged to the edge of G.
(2)(b) I showed John₁ to himself₁ in the mirror	[john, d, he, self, to:p, [mirror, the, in], show, 'v*', [i, d], 'Tpast', c]	(Same as (2a) but (2b) uses the lexical counterpart to G.)
(3)(b) *I showed himself₁ John₁ in the mirror	[john, d, he, self, 'G', [mirror, the, in], show, 'v*', [i, d], 'Tpast', c]	Cannot be derived. DC is he-John, cannot be John-he (John-he would result in stacking he and deriving Condition C violations.) Therefore the stream is the same as for (2a).
(16)(a) *I showed John₁ him₁ in the mirror	[john, d, he, d, 'G', [mirror, the, in], show, 'v*', [i, d], 'Tpast', c]	Does not converge. DC he-John. John not on the stack, not available for G theta-merge. (No LE boundary, no stacking triggered.)
(16)(b) *I showed John₁ to him₁ in the mirror	[john, d, he, d, to:p, [mirror, the, in], show, 'v*', [i, d], 'Tpast', c]	Same analysis as in (16a).
(4) Pictures of himself₁ worry John₁	[john, d, he, self, of, pictures, d, caus_p, worry, caus_v, 'T', c]	Determiner self heads a LE. Doubling constituent (DC) self-he-John triggers stacking of John. CAUS_p does not assign Case to the DC object. TOS John theta-merges to the edge of CAUS_p. CAUS_v values ACC Case for John and also heads a LE. At CAUS_vP, restacking of pictures of himself occurs. [Note: John is not subject to restacking. Stack elements introduced by self are subject to the condition that they may only be stacked once, i.e. must be "used" (merged) in the current LE.] T picks up TOS pictures of himself. [Note: A copy of John inside pictures of himself is raised to edge of T. However,John must be spelled out at edge of CAUS_p.]
(21) Pictures of him₁ worry John₁	[john, d, he, d, of, pictures, d, caus_p, worry, caus_v, 'T', c]	Does not converge. DC he-John. John not on the stack, not available for theta-merge to CAUS_p's edge. (No LE boundary, no stacking triggered.)

Machine Parameters: expand

Animation:
(3)(b) *I showed himself₁ John₁ in the mirror

Derivation:
(3)(b) *I showed himself₁ John₁ in the mirror

Stream:	[[john!D],[d!case!N],[he!D],[self!case!N],[G],[[mirror!D],[the!case!N],[in]],[show],[v*!phi],[[i!D],[d!case!N]],[Tpast!phi],[c]]
Stack (⥥):
SO:	[]

Step 1.

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

Stream:	[[d!case!N],[he!D],[self!case!N],[G],[[mirror!D],[the!case!N],[in]],[show],[v*!phi],[[i!D],[d!case!N]],[Tpast!phi],[c]]
Stack (⥥):
SO:	[john!D]

Step 2.

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:	[[he!D],[self!case!N],[G],[[mirror!D],[the!case!N],[in]],[show],[v*!phi],[[i!D],[d!case!N]],[Tpast!phi],[c]]
Stack (⥥):
SO:	[d!case[d][john]]

Doubling Constitutent (DC) merge

Step 3.

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

Label from [he!D] (head merging with a non-head)

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

Stream:	[[self!case!N],[G],[[mirror!D],[the!case!N],[in]],[show],[v*!phi],[[i!D],[d!case!N]],[Tpast!phi],[c]]
Stack (⥥):	inactive([d!case[d][john]])
SO:	[he!D[he!D][d!case[d][john]]]

Step 4.

Merge [self!case!N] and [he!D[he!D][d!case[d..][john..]]]

Label from [self!case!N] (head merging with a non-head)

Inherit interpretable feature(s) [f(phi,[3,sg,m])] from [he!D[he!D][d!case[d..][john..]]]

[self!case!N] values D on [he!D[he!D][d!case[d..][john..]]]

[he[he][d!case[d..][john..]]] values N on [self!case!N]

Stream:	[[G],[[mirror!D],[the!case!N],[in]],[show],[v*!phi],[[i!D],[d!case!N]],[Tpast!phi],[c]]
Stack (⥥):	inactive([d!case[d][john]])
SO:	[self!case[self][he[he][d!case[d][john]]]]

Step 5.

Local Extent boundary at [self!case[self][he[he..][d..]]]

Inactive stack element inactive([d!case[d][john]]) found

New boundary (b) marker stacked

Restack [d!case[d][john]] onto stack

Stream:	[[G],[[mirror!D],[the!case!N],[in]],[show],[v*!phi],[[i!D],[d!case!N]],[Tpast!phi],[c]]
Stack (⥥):	once([d!case[d][john]]) b
SO:	[self!case[self][he[he][d!case[d][john]]]]

Step 6.

Merge [G] and [self!case[self][he[he..][d..]]]

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

Theta-mark [self!case[self][he[he..][d..]]]

[G] values obq case on [self!case[self][he[he..][d..]]]

Stream:	[[[mirror!D],[the!case!N],[in]],[show],[v*!phi],[[i!D],[d!case!N]],[Tpast!phi],[c]]
Stack (⥥):	once([d!case[d][john]]) b
SO:	[G[G][self[self][he[he][d!case[d][john]]]]]

Step 7.

Begin substream

Stream:	[[mirror!D],[the!case!N],[in]]
Stack (⥥):
SO:	[]

Step 8.

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

Stream:	[[the!case!N],[in]]
Stack (⥥):
SO:	[mirror!D]

Step 9.

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

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

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

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

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

Stream:	[[in]]
Stack (⥥):
SO:	[the!case[the][mirror]]

Step 10.

Merge [in] and [the!case[the][mirror]]

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

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

[in] values obq case on [the!case[the][mirror]]

Stream:	[]
Stack (⥥):
SO:	[in[in][the[the][mirror]]]

End substream, SO [in[in][the[the][mirror]]] re-inserted into main stream

Step 11.

Stream:	[[in[in][the[the][mirror]]],[show],[v*!phi],[[i!D],[d!case!N]],[Tpast!phi],[c]]
Stack (⥥):	once([d!case[d][john]]) b
SO:	[G[G][self[self][he[he][d!case[d][john]]]]]

Step 12.

Internal merge selected

Merge [G[G][self[self..][he..]]] and [d!case[d][john]]

Label from [G[G][self[self..][he..]]] (edge feature)

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

Stream:	[[in[in][the[the][mirror]]],[show],[v*!phi],[[i!D],[d!case!N]],[Tpast!phi],[c]]
Stack (⥥):	[d!case[d][john]] b
SO:	[G[d!case[d][john]][G[G][self[self][he[he][d[d][john]]]]]]

Step 13.

Pair-merge [in[in][the[the][mirror]]] and [G[d!case[d][john]][G[G][self[self][he[he][d[d][john]]]]]]

Stream:	[[show],[v*!phi],[[i!D],[d!case!N]],[Tpast!phi],[c]]
Stack (⥥):	[d!case[d][john]] b
SO:	<[G[d!case[d][john]][G[G][self[self][he[he][d[d][john]]]]]],[in[in][the[the][mirror]]]>

Step 14.

Merge [show] and <[G[d!case[d..][john..]][G[G..][self..]]],[in[in][the[the..][mirror..]]]>

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

Stream:	[[v*!phi],[[i!D],[d!case!N]],[Tpast!phi],[c]]
Stack (⥥):	[d!case[d][john]] b
SO:	[show[show]<[G[d!case[d][john]][G[G][self[self][he[he][d[d][john]]]]]],[in[in][the[the][mirror]]]>]

Step 15.

Merge [v*!phi] and [show[show]<[G[d..][G..]],[in[in..][the..]]>]

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

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

[v*] values acc case on [d!case[d][john]]

Stream:	[[[i!D],[d!case!N]],[Tpast!phi],[c]]
Stack (⥥):	[d[d][john]] b
SO:	[v[v][show[show]<[G[d[d][john]][G[G][self[self][he[he][d[d][john]]]]]],[in[in][the[the][mirror]]]>]]

Step 16.

Begin substream

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

Step 17.

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

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

Step 18.

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

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

Inherit interpretable feature(s) [f(phi,[1,sg,mf])] from [i!D]

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

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

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

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

Step 19.

Stream:	[[d!case[d][i]],[Tpast!phi],[c]]
Stack (⥥):	[d[d][john]] b
SO:	[v[v][show[show]<[G[d[d][john]][G[G][self[self][he[he][d[d][john]]]]]],[in[in][the[the][mirror]]]>]]

Step 20.

Merge [v*[v*][show[show..]<[G..],[in..]>]] and [d!case[d][i]]

Label from [v*[v*][show[show..]<[G..],[in..]>]] (edge feature)

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

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

Stream:	[[Tpast!phi],[c]]
Stack (⥥):	[d!case[d][i]] [d[d][john]] b
SO:	[v[d!case[d][i]][v[v*][show[show]<[G[d[d][john]][G[G][self[self][he[he][d[d][john]]]]]],[in[in][the[the][mirror]]]>]]]

Step 21.

Merge [Tpast!phi] and [v*[d!case[d..][i..]][v*[v*..][show..]]]

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

[d!case[d][i]] values uPhi on [Tpast!phi]

[Tpast] values nom case on [d!case[d][i]]

Stream:	[[c]]
Stack (⥥):	[d[d][i]] [d[d][john]] b
SO:	[Tpast[Tpast][v[d[d][i]][v[v*][show[show]<[G[d[d][john]][G[G][self[self][he[he][d[d][john]]]]]],[in[in][the[the][mirror]]]>]]]]

Step 22.

Internal merge selected

Merge [Tpast[Tpast][v*[d..][v*..]]] and [d[d][i]]

Label from [Tpast[Tpast][v*[d..][v*..]]] (edge feature)

Stream:	[[c]]
Stack (⥥):	[d[d][i]] [d[d][john]] b
SO:	[Tpast[d[d][i]][Tpast[Tpast][v[d[d][i]][v[v*][show[show]<[G[d[d][john]][G[G][self[self][he[he][d[d][john]]]]]],[in[in][the[the][mirror]]]>]]]]]

Step 23.

Merge [c] and [Tpast[d[d..][i..]][Tpast[Tpast..][v*..]]]

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

Stream:	[]
Stack (⥥):	[d[d][i]] [d[d][john]] b
SO:	[c[c][Tpast[d[d][i]][Tpast[Tpast][v[d[d][i]][v[v*][show[show]<[G[d[d][john]][G[G][self[self][he[he][d[d][john]]]]]],[in[in][the[the][mirror]]]>]]]]]]

Step 24.

Local Extent boundary at [c[c][Tpast[d..][Tpast..]]]

New boundary (b) marker stacked

Stream:	[]
Stack (⥥):	b [d[d][i]] [d[d][john]] b
SO:	[c[c][Tpast[d[d][i]][Tpast[Tpast][v[d[d][i]][v[v*][show[show]<[G[d[d][john]][G[G][self[self][he[he][d[d][john]]]]]],[in[in][the[the][mirror]]]>]]]]]]

Parse:

Spell-out:

i -ed(sg) show -acc john -self -obq he in the mirror (after morpheme realization)

i show -ed(sg) john -acc he -obq -self in the mirror (after affix-hop)

i show -ed(sg) john -acc he -obq -self in the mirror (after morpheme realization, stage 2)

i showed john himself in the mirror

One derivation found.

Computational Cost:

Merge: 15, Agree: 14, Unify: 0, Push: 2, Boundaries: 2, Inject: 1

Non-TOS access: 0, Pop: 0, Depth cost: 19

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
Stack depth:	0	0	0	1	1	2	2	0	0	0	0	2	2	2	2	2	0	0	0	2	3	3	3	3	4