Minimalist Machine Derivations

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Examples:

  • Relative clause examples from Sag 1997 (Fong & Ginsburg, ms.) collapse
    Example Instruction stream (clickable) Notes
    (23a) the book which inspired them (Example (24a); Sag 1997: 448
    (23b) *the book which that inspired them     		[they,d,inspire,'v*',[book,which_rel],'Tpast',c_rel,the] Subject relative. DP [book, whichrel] is attracted to the edge of Crel by uRel on Crel. By economy, whichrel values both uT and uRel on Crel, and the T-to-C option is impossible, i.e. *which that in (23b).
    However, whichrel cannot value uD so book will raise further and uD is valued during the merge with the.
    (24) the person whose mother died (Example (24b); Sag 1997: 448)
    		[mother, '\'s', [person, who_rel], die, 'v~unacc', 'Tpast', c_rel, the] Assume whose here is whorel + 's and die is unaccusative, i.e. [[whorel person]['s mother]] is theta-merged at the internal argument position.
    Furthermore, permit uRel on Crel to find iRel on whorel at the edge of possessive 's.
    [[whorel person]['s mother]] is attracted to the edge of Crel. However, whorel cannot value uD on person. Next, person raises and its uD is valued when merged with the.
    (25) the person whose mother's dog died (Example (24d); Sag 1997: 448) [dog, '\'s', [mother, '\'s', [person, who_rel]], die, 'v~unacc', 'Tpast', c_rel, the] Analysis is the same as for (24) above, except we permit uRel on Crel to recursively look for iRel at the edge of possessive 's. Internal argument is [[[whorel person] 's mother]['s dog]].
    (26a) the person whose mother's dog we were (all) fond of (Example (24d); Sag 1997: 448)
    (26b) the person whose mother's dog that we were (all) fond of
    (26c) *the person of whose mother's dog we were (all) fond
    (26d) *the person of whose mother's dog that we were (all) fond     		[dog, '\'s', [mother, '\'s', [person, who_rel]],of,fond,[we,d],v_be,'Tpast',c_rel,the] [[[whorel person] 's mother]['s dog]] is attracted to the edge of Crel by uRel on Crel. We assume, following (25), that uRel on Crel can find recursively iRel at the edge of possessive 's.
    whorel cannot value uD on person. Next, person raises and its uD is valued when merged with the.
    (26b) is predicted as [[[whorel person] 's mother]['s dog]] is not a nominative subject, so economy does not apply. The option of T-to-C generates the complementizer that.
    (26c-d) are blocked by a spellout rule *of who, designed to block *the girl of who friends bought the cake.
    (27a) the person to whom they dedicated the building (Example (24e); Sag 1997: 448)
    (27b) the person whom they dedicated the building to     		[person,who_rel,to,[building,the],dedicate,'v*',[they,d],'Tpast',c_rel,the] We assume dyadic to, i.e. the VP is [dedicate [[the building] [to [whoRel person]]]]. [whoRel person] is attracted to the edge of Crel by uRel on Crel. whorel cannot value uD on person. Next, person raises and its uD is valued when merged with the.
    Pied-piping is permitted as whorel is overt.
    Note: after the two successful derivations, at step 41, the system tries unsuccessfully to employ monadic to with [dedicate [to [whoRel person]]]. The problem is the merge of [the building]. At step 48, the attempted XP-YP pair merge of [the building] fails. At step 59, the corresponding XP-YP set merge fails. After that, there are a further two parallel attempts pushing [to [whoRel person]] onto the stack.
    (28) [Give me] the phone number of the person whose mother's friend's sister's dog's appearance had offended the audience (Example (31a); Sag 1997: 450)
    		[audience,the,offend,'v*',[appearance,'\'s',[dog,'\'s',[sister,'\'s',[friend,'\'s',[mother,'\'s',[person,who_rel]]]]]],perf,v,'Tpast',c_rel,the,of,number,phone,the] The DP with the relative pronoun whorel is deeply embedded recursively within the specifier of possessive 's for the head noun appearance. However, it must be visible to uRel probing.
    Therefore, [[[[[[whorel person]['s mother]]['s friend]]['s sister]]['s dog]]['s appearance]] is attracted to the edge of Crel by uRel on Crel. whorel cannot value uD, so person will raise further to form a new head. Determiner the merges with the NP headed by person, valuing uD on person.
    (29a) [This is] the senator to whose mother's friend's sister's favorite charity the lobbyist had donated a small fortune (Example (31b); Sag 1997: 450)
    (29b) [This is] the senator to whose mother's friend's sister's favorite charity that the lobbyist had donated a small fortune
    (29c) [This is] the senator whose mother's friend's sister's favorite charity the lobbyist had donated a small fortune to
    (29d) [This is] the senator to whose mother's friend's sister's favorite charity that the lobbyist had donated a small fortune
    		[charity,favorite,'\'s',[sister,'\'s',[friend,'\'s',[mother,'\'s',[senator,who_rel]]]],to,[small,fortune,a],donate,'v*',[lobbyist,the],'Tpast',c_rel,the] Similar derivation to example (28). We wh-relativize senator from the lobbyist donated a small fortune to the senator's mother's friend's sister's favorite charity.
    [[[[[whorel senator]['s mother]]['s friend]]['s sister]]['s favorite charity]] is attracted to the edge of Crel by uRel on Crel. whorel cannot value uD, so senator will raise further to form a new head. Determiner the merges with the NP headed by senator, valuing uD on senator.
    There are four parses as the options of inserting the complementizer that and the pied-piping of prepositional to are both freely available.
    (30a) the time when I got drunk
    (30b) *the time when that I got drunk     		[drunk,get,v_unerg,[i,d],'Tpast',[time,when_rel],c_rel,the] Assume the time expression [whenrel time] is merged at TP level for semantic reasons. Both pair merge and set merge options are tested. Because extraction must take place for relativization, only the set merge option can succeed. (Pair merged adjuncts are inaccessible to probing.)
    [whenrel time] is attracted to the edge of Crel by uRel on Crel. whenrel cannot value uD on time. Next, time raises and its uD is valued when merged with the.
    However, whenrel can value uT (as well as uRel) on Crel. By economy, no T-to-C, that in (30b), is possible.
    (31a) the town where I grew up
    (31b) *the town up where I grew     		[up,grow,[town,where_rel],'v_unerg',[i,d],'Tpast',c_rel,the] Assume the location adverbial [whererel town] is merged at the VP level. Both pair merge and set merge options are tested. Because extraction must take place for relativization, only the set merge option can succeed. (Pair merged adjuncts are inaccessible to probing.)
    [whererel town] is attracted to the edge of Crel by uRel on Crel. whererel cannot value uD on town. Next, town raises and its uD is valued when merged with the.
    However, whererel can value uT (as well as uRel) on Crel. By economy, no T-to-C (that) is possible.
    Finally, up does not head a PP with complement [whererel town] (merged at VP level instead). Therefore no pied-piping, as in (31b), is possible.
    (33a) someone to rely on
    (33b) *someone on to rely     		[someone, d_rel, on, rely, 'v*', ['PRO', d0], 'Tinf', c_rel, d] [drel someone] is attracted to the edge of Crel by uRel on Crel. drel cannot value uD, so someone will raise further. Tinf checks uT on Crel. (drel cannot value uT on Crel, uT is valued by Tinf instead.
    Pied-piping is blocked by the empty determiner drel, cf. overt whorel in (35a).
    (Note: this lexicon contains both simple prepositional on and dyadic on, e.g. put the book on the shelf. Step 17 onwards using dyadic on fails to derive.)
    (34a) someone for you to rely on
    (34b) *someone on for you to rely     		[someone, d_rel, on, rely, 'v*', [you, d], 'Tinf', for, c_rel, d] Assume complementizer for generally licenses an overt subject, you, by assigning Case, cf. PRO in (33a). Crel, containing uRel, piggy-backs onto for, attracting [drel someone] to its edge.
    Covert drel in [on [drel someone]] incompatible with pied-piping of on, so (34b) is blocked.
    As described in (33a), someone will raise further and merge with covert d.
    (35a) the baker in whom to place your trust (Example (63a); Sag 1997:461)
    (35b) *the baker whom to place your trust in (Example (63d); Sag 1997:461)     		[baker, who_rel, in, [ trust, '\'s', [you, d]], place, 'v*', ['PRO', d0], 'Tinf', c_rel, the] Both (35a-b) are predicted to be grammatical here, i.e. pied-piping is permitted. (Judgements shown are from Sag.)
    Assume in is dyadic, i.e. VP structure is [place [your trust [in [who baker]]]]. (Note: the derivations with dyadic in begin at step 51 and end at step 103. Simple preposition in is tried first, but fails to converge at step 50.)
    Either [in [whorel baker]] (for pied-piping) or [whorel baker], the internal argument of in, may be attracted to edge of Crel by uRel on Crel.
    NB: whorel is defective, i.e. it doesn't value the uD feature on baker. Therefore, baker raises from edge of C and its uD feature is checked by determiner the.
    (36a) the baker to place your trust in
    (36b) *the baker in to place your trust     		[baker, d_rel, in, [ trust, '\'s', [you, d]], place, 'v*', ['PRO', d0], 'Tinf', c_rel, the] No overt whorel here, cf. (35a-b). Covert drel is used instead, i.e. internal argument of in is [drel baker]. [drel baker] is attracted to the edge of Crel by uRel on Crel. Pied-piping is not an option since drel is an empty category, cf. (35b).
    drel cannot value uD so baker will raise further and its uD will be checked by the.
    Assume uT on Crel is valued by Tinf.
    (Note: the derivation with dyadic in begins at step 28 and concludes at step 54. Simple preposition in is tried first, but fails to converge at steps 16 and 27 for pair and set merge, respectively.)
    (37) the person for us to visit (Example (75b); Sag 1997: 464)
    		[person, d_rel, visit, 'v*', [we, d], 'Tinf', for, c_rel, the] Similar to (34a), assume complementizer for generally licenses an overt subject, we, in a tenseless clause by assigning Case. Crel, containing uRel, piggy-backs onto the complementizer for, attracting [drel person] to its edge.
    drel cannot value uD on person. The head person raises further and merges with the, which values person's uD feature.
    (38) the person to visit (Example (75c); Sag 1997: 464) [person, d_rel, visit, 'v*', ['PRO', d0], 'Tinf', c_rel, the] Compared with (37), there is no for with an overt subject; instead, we assume the covert subject is PRO.
    [drel person] is attracted to the edge of Crel by uRel on Crel. drel cannot value uD on person. The head person raises further and merges with the, which values person's uD feature.
    • Machine Parameters: expand

    Animation:
    (34a) someone for you to rely on
    (34b) *someone on for you to rely

    Derivation:
    (34a) someone for you to rely on
    (34b) *someone on for you to rely

    Stream:[[someone!D],[drel!case!N],[on],[rely],[v*!phi],[[you!D],[d!case!N]],[Tinf!phi],[for!phi],[crel!rel!T!phi],[d!case!N]]
    Stack (⥥):
    SO:[]

    Step 1.

    Head of stream [someone!D] is the initial SO
    Stream:[[drel!case!N],[on],[rely],[v*!phi],[[you!D],[d!case!N]],[Tinf!phi],[for!phi],[crel!rel!T!phi],[d!case!N]]
    Stack (⥥):
    SO:[someone!D]

    Step 2.

    Merge [drel!case!N] and [someone!D]
    Label from [drel!case!N] (syntactic head with an unvalued uF)
    Inherit interpretable feature(s) [f(phi,[3,sg,n])] from [someone!D]
    [someone!D] values N on [drel!case!N]
    Push [someone!D] (unvalued uF) onto stack
    Stream:[[on],[rely],[v*!phi],[[you!D],[d!case!N]],[Tinf!phi],[for!phi],[crel!rel!T!phi],[d!case!N]]
    Stack (⥥):[someone!D]
    SO:[drel!case[drel][someone!D]]

    Step 3.

    Merge [on] and [drel!case[drel][someone!D]]
    Label from [on] (syntactic head merging with a non-head)
    Theta-mark [drel!case[drel][someone!D]]
    Push [drel!case[drel][someone!D]] (unvalued uF) onto stack
    Stream:[[rely],[v*!phi],[[you!D],[d!case!N]],[Tinf!phi],[for!phi],[crel!rel!T!phi],[d!case!N]]
    Stack (⥥):[drel!case[drel][someone!D]]
    [someone!D]
    SO:[on[on][drel!case[drel][someone!D]]]

    Step 4.

    Merge [rely] and [on[on][drel!case[drel..][someone..]]]
    Label from [rely] (syntactic head merging with a non-head)
    Stream:[[v*!phi],[[you!D],[d!case!N]],[Tinf!phi],[for!phi],[crel!rel!T!phi],[d!case!N]]
    Stack (⥥):[drel!case[drel][someone!D]]
    [someone!D]
    SO:[rely[rely][on[on][drel!case[drel][someone!D]]]]

    Step 5.

    Merge [v*!phi] and [rely[rely][on[on..][drel..]]]
    Label from [v*!phi] (syntactic head merging with a non-head)
    [drel!case[drel][someone!D]] values uPhi on [v*!phi]
    [v*] values acc case on [drel!case[drel][someone!D]]
    Stream:[[[you!D],[d!case!N]],[Tinf!phi],[for!phi],[crel!rel!T!phi],[d!case!N]]
    Stack (⥥):[drel[drel][someone!D]]
    [someone!D]
    SO:[v*[v*][rely[rely][on[on][drel[drel][someone!D]]]]]

    Step 6.

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

    Step 7.

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

    Step 8.

    Merge [d!case!N] and [you!D]
    Label from [d!case!N] (syntactic head with an unvalued uF)
    Inherit interpretable feature(s) [f(phi,[2,pl,mf])] from [you!D]
    [d!case!N] values D on [you!D]
    [you] values N on [d!case!N]
    Stream:[]
    Stack (⥥):
    SO:[d!case[d][you]]
    End substream, SO [d!case[d][you]] re-inserted into main stream

    Step 9.

    Stream:[[d!case[d][you]],[Tinf!phi],[for!phi],[crel!rel!T!phi],[d!case!N]]
    Stack (⥥):[drel[drel][someone!D]]
    [someone!D]
    SO:[v*[v*][rely[rely][on[on][drel[drel][someone!D]]]]]

    Step 10.

    Merge [v*[v*][rely[rely..][on..]]] and [d!case[d][you]]
    Label from [v*[v*][rely[rely..][on..]]] (edge feature)
    Theta-mark [d!case[d][you]]
    Push [d!case[d][you]] (unvalued uF) onto stack
    Stream:[[Tinf!phi],[for!phi],[crel!rel!T!phi],[d!case!N]]
    Stack (⥥):[d!case[d][you]]
    [drel[drel][someone!D]]
    [someone!D]
    SO:[v*[d!case[d][you]][v*[v*][rely[rely][on[on][drel[drel][someone!D]]]]]]

    Step 11.

    Merge [Tinf!phi] and [v*[d!case[d..][you..]][v*[v*..][rely..]]]
    Label from [Tinf!phi] (syntactic head merging with a non-head)
    [d!case[d][you]] values uPhi on [Tinf!phi]
    Stream:[[for!phi],[crel!rel!T!phi],[d!case!N]]
    Stack (⥥):[d!case[d][you]]
    [drel[drel][someone!D]]
    [someone!D]
    SO:[Tinf[Tinf][v*[d!case[d][you]][v*[v*][rely[rely][on[on][drel[drel][someone!D]]]]]]]

    Step 12.

    Internal merge selected
    Merge [Tinf[Tinf][v*[d..][v*..]]] and [d!case[d][you]]
    Label from [Tinf[Tinf][v*[d..][v*..]]] (edge feature)
    Stream:[[for!phi],[crel!rel!T!phi],[d!case!N]]
    Stack (⥥):[d!case[d][you]]
    [drel[drel][someone!D]]
    [someone!D]
    SO:[Tinf[d!case[d][you]][Tinf[Tinf][v*[d[d][you]][v*[v*][rely[rely][on[on][drel[drel][someone!D]]]]]]]]

    Step 13.

    Merge [for!phi] and [Tinf[d!case[d..][you..]][Tinf[Tinf..][v*..]]]
    Label from [for!phi] (syntactic head merging with a non-head)
    [d!case[d][you]] values uPhi on [for!phi]
    [for] values obq case on [d!case[d][you]]
    Stream:[[crel!rel!T!phi],[d!case!N]]
    Stack (⥥):[d[d][you]]
    [drel[drel][someone!D]]
    [someone!D]
    SO:[for[for][Tinf[d[d][you]][Tinf[Tinf][v*[d[d][you]][v*[v*][rely[rely][on[on][drel[drel][someone!D]]]]]]]]]

    Step 14.

    Local Extent boundary at [for[for][Tinf[d..][Tinf..]]]
    Stack element [drel[drel][someone!D]] with unvalued uF found
    Stack element [someone!D] with unvalued uF found
    New boundary (b) marker stacked
    Restack [someone!D] onto stack
    Restack [drel[drel][someone!D]] onto stack
    Stream:[[crel!rel!T!phi],[d!case!N]]
    Stack (⥥):[drel[drel][someone!D]]
    [someone!D]
    b
    [d[d][you]]
    SO:[for[for][Tinf[d[d][you]][Tinf[Tinf][v*[d[d][you]][v*[v*][rely[rely][on[on][drel[drel][someone!D]]]]]]]]]

    Step 15.

    Merge [crel!rel!T!phi] and [for[for][Tinf[d..][Tinf..]]]
    Label from [crel!rel!T!phi] (syntactic head merging with a non-head)
    [drel[drel][someone!D]] values rel on [crel!rel!T!phi]
    Relativized TOS search for iF(T) skipping [drel[drel][someone!D]]
    Relativized TOS search for iF(T) skipping [someone!D]
    [crel!T!phi] attracts [for[for][Tinf[d..][Tinf..]]]
    [drel[drel][someone!D]] values phi on [crel!phi] (economy)
    [crel] values obq case on [drel[drel][someone!D]]
    Internal merge selected
    Merge [crel[crel][for[for..][Tinf..]]] and [for]
    Label from [crel[crel][for[for..][Tinf..]]] (edge feature)
    Merge [crel[for][crel[crel..][for..]]] and [drel[drel][someone!D]]
    Label from [crel[for][crel[crel..][for..]]] (edge feature)
    Stream:[[d!case!N]]
    Stack (⥥):[drel[drel][someone!D]]
    [someone!D]
    b
    [d[d][you]]
    SO:[crel[drel[drel][someone!D]][crel[for][crel[crel][for[for][Tinf[d[d][you]][Tinf[Tinf][v*[d[d][you]][v*[v*][rely[rely][on[on][drel[drel][someone!D]]]]]]]]]]]]

    Step 16.

    Local Extent boundary at [crel[drel[drel..][someone..]][crel[for..][crel..]]]
    Stack element [drel[drel][someone!D]] with unvalued uF found
    Stack element [someone!D] with unvalued uF found
    New boundary (b) marker stacked
    Restack [someone!D] onto stack
    Restack [drel[drel][someone!D]] onto stack
    Stream:[[d!case!N]]
    Stack (⥥):[drel[drel][someone!D]]
    [someone!D]
    b
    b
    [d[d][you]]
    SO:[crel[drel[drel][someone!D]][crel[for][crel[crel][for[for][Tinf[d[d][you]][Tinf[Tinf][v*[d[d][you]][v*[v*][rely[rely][on[on][drel[drel][someone!D]]]]]]]]]]]]

    Step 17.

    Merge [someone!D] and [crel[drel[drel..][someone..]][crel[for..][crel..]]]
    Label from [someone!D] (syntactic head merging with a non-head)
    Stream:[[d!case!N]]
    Stack (⥥):b
    b
    [d[d][you]]
    SO:[someone!D[someone!D][crel[drel[drel][someone!D]][crel[for][crel[crel][for[for][Tinf[d[d][you]][Tinf[Tinf][v*[d[d][you]][v*[v*][rely[rely][on[on][drel[drel][someone!D]]]]]]]]]]]]]

    Step 18.

    Merge [d!case!N] and [someone!D[someone!D][crel[drel..][crel..]]]
    Label from [d!case!N] (syntactic head merging with a non-head)
    Inherit interpretable feature(s) [f(phi,[3,sg,n])] from [someone!D[someone!D][crel[drel..][crel..]]]
    [d!case!N] values D on [someone!D[someone!D][crel[drel..][crel..]]]
    [someone[someone][crel[drel..][crel..]]] values N on [d!case!N]
    Stream:[]
    Stack (⥥):b
    b
    [d[d][you]]
    SO:[d!case[d][someone[someone][crel[drel[drel][someone]][crel[for][crel[crel][for[for][Tinf[d[d][you]][Tinf[Tinf][v*[d[d][you]][v*[v*][rely[rely][on[on][drel[drel][someone]]]]]]]]]]]]]]

    Parse:
    Spell-out:
    someone for -obq you to rely on (after morpheme realization)
    someone for you -obq to rely on (after affix-hop)
    someone for you -obq to rely on (after morpheme realization, stage 2)
    someone for you to rely on  

    Stream:[[someone!D],[drel!case!N],[on],[rely],[v*!phi],[[you!D],[d!case!N]],[Tinf!phi],[for!phi],[crel!rel!T!phi],[d!case!N]]
    Stack (⥥):
    SO:[]

    Step 19.

    Head of stream [someone!D] is the initial SO
    Stream:[[drel!case!N],[on],[rely],[v*!phi],[[you!D],[d!case!N]],[Tinf!phi],[for!phi],[crel!rel!T!phi],[d!case!N]]
    Stack (⥥):
    SO:[someone!D]

    Step 20.

    Merge [drel!case!N] and [someone!D]
    Label from [drel!case!N] (syntactic head with an unvalued uF)
    Inherit interpretable feature(s) [f(phi,[3,sg,n])] from [someone!D]
    [someone!D] values N on [drel!case!N]
    Push [someone!D] (unvalued uF) onto stack
    Stream:[[on],[rely],[v*!phi],[[you!D],[d!case!N]],[Tinf!phi],[for!phi],[crel!rel!T!phi],[d!case!N]]
    Stack (⥥):[someone!D]
    SO:[drel!case[drel][someone!D]]

    Step 21.

    Merge [on] and [drel!case[drel][someone!D]]
    Label from [on] (syntactic head merging with a non-head)
    Theta-mark [drel!case[drel][someone!D]]
    [on] values obq case on [drel!case[drel][someone!D]]
    Push [drel[drel][someone!D]] (unvalued uF) onto stack
    Stream:[[rely],[v*!phi],[[you!D],[d!case!N]],[Tinf!phi],[for!phi],[crel!rel!T!phi],[d!case!N]]
    Stack (⥥):[drel[drel][someone!D]]
    [someone!D]
    SO:[on[on][drel[drel][someone!D]]]

    Step 22.

    Relativized TOS search for unvaluediF(theta) skipping [drel[drel][someone!D]]
    Relativized TOS search for unvaluediF(theta) skipping [someone!D]
    Internal merge to edge of [on[on][drel[drel][someone!D]]] failed
    No possible action for stream [[rely],[v*!phi],[[you!D],[d!case!N]],[Tinf!phi],[for!phi],[crel!rel!T!phi],[d!case!N]] and [on[on][drel[drel..][someone..]]]
    One derivation found.
    Computational Cost:
    Merge: 16, Agree: 16, Unify: 0, Push: 5, Boundaries: 2, Inject: 4
    Non-TOS access: 4, Pop: 0, Depth cost: 27
    Step:012345678910111213141516171819202122
    Stack depth:00122200023333445330012

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