Minimalist Machine Derivations

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Examples:

  • Computation with doubling constituents: Pronouns and antecedents in Phase Theory. (Fong & Ginsburg, 2012). collapse
    Example Instruction stream (clickable) Notes
    (4)(a) John1 thinks he1 is smart
    John1 thinks that he1 is smart    		 [john, d, he, d, smart, v_be, 'T', c_e, think, v_unerg, 'T', c] Doubling constituent (DC) he-John.
    Local Extent (LE) boundary (b) at embedded CeP triggers stacking of John.
    vunerg picks up TOS John.
    Two derivations due to T-to-C movement (Pesetsky & Torrego, 2001).
    (5)(a) *John1 praises him1 [john, d, he, d, praise, 'v*', 'T', c] Does not converge.
    DC he-John.
    John not on the stack, not available for theta-merge.
    (No LE boundary, no stacking triggered.)
    (6)(a) John1 praises himself1 [john, d, he, self, praise, 'v*', 'T', c] Determiner self heads a LE.
    Completion of DC self-he-John triggers stacking of John.
    [Note: 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. See example (8a).]
    v* picks up TOS John.
    (7)(a) John1 thinks that Mary likes him1
    John1 thinks Mary likes him1    		 [john, d, he, d, like, 'v*', [mary, d], 'T', c_e, think, v_unerg, 'T', c] DC he-John.
    LE boundary (b) at embedded CeP triggers stacking of John.
    vunerg merges TOS John to its edge.
    Two derivations due to T-to-C movement (Pesetsky & Torrego, 2001).
    (8)(a) *John1 thinks that Mary likes himself1 [john, d, he, self, like, 'v*', [mary, d], 'T', c_e, think, v_unerg, 'T', c] Does not converge.
    LE boundary (b) at DC self-he-John stacking of John.
    [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.]
    Edge of v* preferentially merges Mary from the stream.
    At the next LE boundary, embedded CeP, John cannot be re-stacked, and falls behind the LE boundary (b).
    Search past a LE boundary (b) is not permitted.
    Derivation crashes since edge of matrix v* cannot see John on the stack.
    (29) John1 thinks that Peter thinks that Mary thinks that Bill likes him1 [john, d, he, d, like, 'v*', [bill, d], 'T', c_e, think, v_unerg, [mary, d], 'T', c_e, think, v_unerg, [peter, d], 'T', c_e, think, v_unerg, 'T', c] DC he-John.
    CeP triggers stacking of John.
    v* preferentially merges from the stream: Mary and Peter will be preferred over John on the stack.
    At each intermediate LE boundary, CeP, John will be re-stacked in front of the boundary mark (b).
    Matrix vunerg picks up TOS John.
    (No competition from the stream at this point.)
    Eight derivations due to T-to-C movement for each sub-clause (Pesetsky & Torrego, 2001).
    (32) ?John thinks that Peter1 thinks that Mary thinks that Bill likes him1 [peter, d, he, d, like, 'v*', [bill, d], 'T', c_e, think, v_unerg, [mary, d], 'T', c_e, think, v_unerg, 'T', c_e, think, v_unerg, [john, d], 'T', c] DC he-Peter.
    Derivation proceeds as in (29) above, except no competition from the stream for v* theta-merge in 1st embedded clause (cf. matrix v*).
    (38) John1 considers himself1 to be intelligent [john, d, he, self, intelligent, v_be, 'Tinf', consider, 'v*', 'T', c] DC self-he-John forms a LE boundary.
    John is stacked (but cannot be restacked).
    Complement of ECM verb consider is not a CP, and thus not a LE boundary.
    Matrix v* picks up TOS John .
    (9)(a) *John1 considers him1 to be intelligent [john, d, he, d, intelligent, v_be, 'Tinf', consider, 'v*', 'T', c] Does not converge.
    DC he-John.
    The complement of ECM verb consider is not a LE boundary.
    No stacking triggered.
    John not on stack, not available for theta-merge at matrix v*.
    (40) *John1 thinks heself1 is smart [john, d, he, self, smart, v_be, 'T', c_e, think, v_unerg, 'T', c] Does not converge.
    DC self-he-John forms a LE boundary.
    John is stacked (but not permitted to be restacked).
    At the next LE boundary, CeP, John cannot be restacked, and falls behinds the boundary marker (b).
    Matrix vunerg fails to find John on the stack.
    (42)(a) John1 likes his1 dog [dog, '\'s', [john, d, he, d], like, 'v*', 'T', c] DC he-John.
    's heads a LE.
    DP he-John's dog triggers stacking of John.
    Merge likes and he-John's dog triggers stacking of he-John's dog (uCase).
    [Note: if [A .. [B ..]] is pushed onto the stack, and [B ..] from a substream is already on the stack, A subsumes B and renders B unavailable on the stack. (See On Phases examples.) ]
    John is a subconstituent of he-John's dog but John, although formed in a substream, is only stacked visibly in the mainstream.
    Constraint does not apply.
    Matrix v* picks up TOS John.
    (42)(b) *John1 likes himself1's dog [dog, '\'s', [john, d, he, self], like, 'v*', 'T', c] DC self-he-John marks a LE boundary.
    John is stacked (but not permitted to be restacked).
    's heads the next LE boundary.
    Since John cannot be restacked, it falls behind the boundary marker (b) and is inaccessible to matrix v*.
    (45)(a) *Hannah1 found a picture of her1 [hannah, d, she, d, of, picture, a, find, 'v*', 'Tpast', c] Does not converge.
    DC she-Hannah.
    Hannah not on the stack, not available for theta-merge.
    (No LE boundary, no stacking triggered.)
    (45)(b) Hannah1 found a picture of herself1 [hannah, d, she, self, of, picture, a, find, 'v*', 'Tpast', c] Determiner self heads a LE.
    Completion of DC self-she-Hannah triggers stacking of Hannah.
    v* picks up TOS Hannah.
    (45)(c) *Hannah found Peter1's picture of him1 [peter, d, he, d, of, picture, '\'s', find, 'v*', [hannah, d], 'Tpast', c] Does not converge.
    DC he-Peter.
    Peter not on the stack, not available for theta-merge.
    (No LE boundary, no stacking triggered.)
    (45)(d) Hannah found Peter1's picture of himself1 [peter, d, he, self, of, picture, '\'s', find, 'v*', [hannah, d], 'Tpast', c] Determiner self heads a LE.
    DP self-he-Peter triggers stacking of Peter.
    's edge theta-merges with TOS Peter.
    (45)(e) Hannah1 found Peter's picture of her1 [hannah, d, she, d, of, picture, '\'s', [peter, d], find, 'v*','Tpast', c] DC she-Hannah.
    's heads a LE.
    DP Peter's picture of her-Hannah triggers stacking of Hannah.
    v* picks up TOS Hannah.
    (45)(f) Hannah1 found Peter's picture of herself1 [hannah, d, she, self, of, picture, '\'s', [peter, d], find, 'v*','Tpast', c] Does not converge.
    Determiner self heads a LE.
    Completion of DC self-she-Hannah triggers stacking of Hannah.
    [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.]
    's heads a LE Peter's picture of self-she-Hannah.
    Since Hannah cannot be restacked, it falls behind the boundary marker (b) and is inaccessible to matrix v*.
    Extra test cases
    (x1) John1 thinks he1 likes Mary
    John1 thinks that he1 likes Mary     		[mary, d, like, 'v*', [john, d, he, d], 'T', c_e, think, v_unerg, 'T', c] DC he-John.
    LE boundary at CeP triggers stacking of John.
    vunerg picks up TOS John.
    Two derivations due to T-to-C movement (Pesetsky & Torrego, 2001).
    • Machine Parameters: expand

    Animation:
    (42)(b) *John1 likes himself1's dog

    Derivation:
    (42)(b) *John1 likes himself1's dog

    Stream:[[dog!D],['s!case!N],[[john!D],[d!case!N],[he!D],[self!case!N]],[like],[v*!phi],[T!phi],[c]]
    Stack (⥥):
    SO:[]

    Step 1.

    Head of stream [dog!D] is the initial SO
    Stream:[['s!case!N],[[john!D],[d!case!N],[he!D],[self!case!N]],[like],[v*!phi],[T!phi],[c]]
    Stack (⥥):
    SO:[dog!D]

    Step 2.

    Merge ['s!case!N] and [dog!D]
    Label from ['s!case!N] (head with an unvalued uF)
    Inherit interpretable feature(s) [f(phi,[3,sg,n])] from [dog!D]
    ['s!case!N] values D on [dog!D]
    [dog] values N on ['s!case!N]
    Stream:[[[john!D],[d!case!N],[he!D],[self!case!N]],[like],[v*!phi],[T!phi],[c]]
    Stack (⥥):
    SO:['s!case['s][dog]]

    Step 3.

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

    Step 4.

    Head of stream [john!D] is the initial SO
    Stream:[[d!case!N],[he!D],[self!case!N]]
    Stack (⥥):
    SO:[john!D]

    Step 5.

    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]]
    Stack (⥥):
    SO:[d!case[d][john]]
    Doubling Constitutent (DC) merge

    Step 6.

    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]]
    Stack (⥥):inactive([d!case[d][john]])
    SO:[he!D[he!D][d!case[d][john]]]

    Step 7.

    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:[]
    Stack (⥥):inactive([d!case[d][john]])
    SO:[self!case[self][he[he][d!case[d][john]]]]

    Step 8.

    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:[]
    Stack (⥥):once([d!case[d][john]])
    b
    SO:[self!case[self][he[he][d!case[d][john]]]]
    End substream, SO [self!case[self][he[he][d!case[d][john]]]] re-inserted into main stream
    Substream stack [once([d!case[d][john]]),b] merged with main stack

    Step 9.

    Stream:[[self!case[self][he[he][d!case[d][john]]]],[like],[v*!phi],[T!phi],[c]]
    Stack (⥥):once([d!case[d][john]])
    b
    SO:['s!case['s][dog]]

    Step 10.

    Theta-mark [self!case[self][he[he..][d..]]]
    ['s!case['s][dog]] values gen case on [self!case[self][he[he..][d..]]]
    Merge ['s!case['s][dog]] and [self[self][he[he..][d..]]]
    Label from ['s!case['s][dog]] (edge feature)
    Stream:[[like],[v*!phi],[T!phi],[c]]
    Stack (⥥):once([d!case[d][john]])
    b
    SO:['s!case[self[self][he[he][d!case[d][john]]]]['s['s][dog]]]

    Step 11.

    Local Extent boundary at ['s!case[self[self..][he..]]['s['s..][dog..]]]
    New boundary (b) marker stacked
    Stream:[[like],[v*!phi],[T!phi],[c]]
    Stack (⥥):b
    once([d!case[d][john]])
    b
    SO:['s!case[self[self][he[he][d!case[d][john]]]]['s['s][dog]]]

    Step 12.

    Merge [like] and ['s!case[self[self..][he..]]['s['s..][dog..]]]
    Label from [like] (head merging with a non-head)
    Theta-mark ['s!case[self[self..][he..]]['s['s..][dog..]]]
    Subconstituent [d!case[d][john]] from a substream removed from stack, ['s!case[self[self..][he..]]['s['s..][dog..]]] subsumes it
    Push ['s!case[self[self..][he..]]['s['s..][dog..]]] (unvalued uF) onto stack
    Stream:[[v*!phi],[T!phi],[c]]
    Stack (⥥):['s!case[self[self][he[he][d!case[d][john]]]]['s['s][dog]]]
    b
    b
    SO:[like[like]['s!case[self[self][he[he][d!case[d][john]]]]['s['s][dog]]]]

    Step 13.

    Merge [v*!phi] and [like[like]['s!case[self..]['s..]]]
    Label from [v*!phi] (head merging with a non-head)
    ['s!case[self[self..][he..]]['s['s..][dog..]]] values uPhi on [v*!phi]
    [v*] values acc case on ['s!case[self[self..][he..]]['s['s..][dog..]]]
    Stream:[[T!phi],[c]]
    Stack (⥥):['s[self[self][he[he][d!case[d][john]]]]['s['s][dog]]]
    b
    b
    SO:[v*[v*][like[like]['s[self[self][he[he][d!case[d][john]]]]['s['s][dog]]]]]

    Step 14.

    Relativized TOS search for unvaluediF(theta) skipping ['s[self[self..][he..]]['s['s..][dog..]]]
    Internal merge for v [v*[v*][like[like]['s[self[self][he[he][d!case[d][john]]]]['s['s][dog]]]]] failed
    No possible action for stream [[T!phi],[c]] and [v*[v*][like[like..]['s..]]]
    No derivations found.
    Computational Cost:
    Merge: 7, Agree: 9, Unify: 0, Push: 2, Boundaries: 2, Inject: 1
    Non-TOS access: 1, Pop: 0, Depth cost: 9
    Step:012345678910111213
    Stack depth:00000011222333

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