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.
    CAUSp does not assign Case to the DC object.
    TOS John theta-merges to the edge of CAUSp.
    CAUSv values ACC Case for John and also heads a LE.
    At CAUSvP, 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 CAUSp.]
    (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 CAUSp's edge.
    (No LE boundary, no stacking triggered.)
  • Machine Parameters: expand

    Animation:
    (16)(a) *I showed John1 him1 in the mirror

    Derivation:
    (16)(a) *I showed John1 him1 in the mirror

    Stream:[[john!D],[d!case!N],[he!D],[d!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],[d!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],[d!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:[[d!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 [d!case!N] and [he!D[he!D][d!case[d..][john..]]]
    Label from [d!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..]]]
    [d!case!N] values D on [he!D[he!D][d!case[d..][john..]]]
    [he[he][d!case[d..][john..]]] values N on [d!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:[d!case[d][he[he][d!case[d][john]]]]

    Step 5.

    Merge [G] and [d!case[d][he[he..][d..]]]
    Label from [G] (head merging with a non-head)
    Theta-mark [d!case[d][he[he..][d..]]]
    [G] values obq case on [d!case[d][he[he..][d..]]]
    Stream:[[[mirror!D],[the!case!N],[in]],[show],[v*!phi],[[i!D],[d!case!N]],[Tpast!phi],[c]]
    Stack (⥥):inactive([d!case[d][john]])
    SO:[G[G][d[d][he[he][d!case[d][john]]]]]

    Step 6.

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

    Step 7.

    Head of stream [mirror!D] is the initial SO
    Stream:[[the!case!N],[in]]
    Stack (⥥):
    SO:[mirror!D]

    Step 8.

    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 9.

    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 10.

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

    Step 11.

    Internal merge to edge of [G[G][d[d][he[he][d!case[d][john]]]]] failed
    No possible action for stream [[in[in][the[the][mirror]]],[show],[v*!phi],[[i!D],[d!case!N]],[Tpast!phi],[c]] and [G[G][d[d..][he..]]]
    No derivations found.
    Computational Cost:
    Merge: 6, Agree: 8, Unify: 0, Push: 1, Boundaries: 0, Inject: 0
    Non-TOS access: 0, Pop: 0, Depth cost: 0
    Step:012345678910
    Stack depth:00011100001

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